Showing papers in "Journal of High Energy Physics in 2002"
TL;DR: In this paper, a new generation of parton distribution functions with increased precision and quantitative estimates of uncertainties is presented, using a recently developed eigenvector-basis approach to the hessian method, which provides the means to quickly estimate the uncertainties of a wide range of physical processes at these high-energy hadron colliders, based on current knowledge of the parton distributions.
Abstract: A new generation of parton distribution functions with increased precision and quantitative estimates of uncertainties is presented. This work signiflcantly extends previous CTEQ and other global analyses on two fronts: (i) a full treatment of available experimental correlated systematic errorsforbothnewandolddata sets; (ii) asystematic and pragmatic treatment of uncertainties of the parton distributions and their physical predictions, using a recently developed eigenvector-basis approach to the hessian method. The new gluon distribution is considerably harder than that of previous standard flts. A numberofphysicsissues,particularlyrelatingtothebehaviorofthegluondistribution,are addressedinmorequantitativetermsthanbefore. Extensiveresultsontheuncertaintiesof parton distributions at various scales, and on parton luminosity functions at the Tevatron RunII and the LHC, are presented. The latter provide the means to quickly estimate the uncertainties of a wide range of physical processes at these high-energy hadron colliders, basedoncurrentknowledgeofthepartondistributions. Inparticular, theuncertaintieson the production cross sections of the W, Z at the Tevatron and the LHC are estimated to be§4% and§5%, respectively, and that of a light Higgs at the LHC to be§5%.
4,427 citations
TL;DR: In this paper, the string spectrum in flat space and pp-waves arises from the large-N limit, at fixed g2YM, of U(N) = 4 super Yang Mills.
Abstract: We explain how the string spectrum in flat space and pp-waves arises from the large-N limit, at fixed g2YM, of U(N) = 4 super Yang Mills. We reproduce the spectrum by summing a subset of the planar Feynman diagrams. We give a heuristic argument for why we can neglect other diagrams. We also discuss some other aspects of pp-waves and we present a matrix model associated to the DLCQ description of the maximally supersymmetric eleven dimensional pp-waves.
2,181 citations
TL;DR: In this paper, the authors proposed a method for matching the next-to-leading order (NLO) calculation of a given QCD process with a parton shower Monte Carlo (MC) simulation.
Abstract: We propose a method for matching the next-to-leading order (NLO) calculation of a given QCD process with a parton shower Monte Carlo (MC) simulation. The method has the following features: fully exclusive events are generated, with hadronization according to the MC model; total exclusive rates are accurate to NLO; NLO results for distributions are recovered upon expansion in ?s; hard emissions are treated as in NLO computations while soft/collinear emissions are handled by the MC simulation, with the same logarithmic accuracy as the MC; and matching between the hard- and soft/collinear-emission regions is smooth. A fraction of events with negative weight is generated, but unweighting remains possible with reasonable efficiency. The method is clarified using a simple toy model, and illustrated by application to the hadroproduction of W+W? pairs.
2,101 citations
TL;DR: In this paper, a prescription for computing Minkowski-space correlators from AdS/CFT correspondence was formulated and shown to give the correct retarded propagators at zero temperature in four dimensions, as well as at finite temperature in two dimensions.
Abstract: We formulate a prescription for computing Minkowski-space correlators from AdS/CFT correspondence. This prescription is shown to give the correct retarded propagators at zero temperature in four dimensions, as well as at finite temperature in the two-dimensional conformal field theory dual to the BTZ black hole. Using the prescription, we calculate the Chern-Simons diffusion constant of the finite-temperature = 4 supersymmetric Yang-Mills theory in the strong coupling limit. We explain why the quasinormal frequencies of the asymptotically AdS background correspond to the poles of the retarded Green's function of the boundary conformal field theory.
1,478 citations
TL;DR: In this paper, the correlation functions of R-charge currents and components of the stress energy tensor in the strongly coupled large-N finite-temperature = 4 supersymmetric Yang-Mills theory were computed.
Abstract: We compute the correlation functions of R-charge currents and components of the stress-energy tensor in the strongly coupled large-N finite-temperature = 4 supersymmetric Yang-Mills theory, following a recently formulated minkowskian AdS/CFT prescription. We observe that in the long-distance, low-frequency limit, such correlators have the form dictated by hydrodynamics. We deduce from the calculations the R-charge diffusion constant and the shear viscosity. The value for the latter is in agreement with an earlier calculation based on the Kubo formula and absorption by black branes.
1,057 citations
TL;DR: In this article, the back-reaction properties of D-branes are analyzed in the context of supersymmetric examples, and it is shown that most of these properties are not necessary to go beyond the probe limit in which one neglects the backreaction of the flavor.
Abstract: Coupling fundamental quarks to QCD in the dual string representation corresponds to adding the open string sector. Flavors therefore should be represented by space-time filling D-branes in the dual 5d closed string background. This requires several interesting properties of D-branes in AdS. D-branes have to be able to end in thin air in order to account for massive quarks, which only live in the UV region. They must come in distinct sets, representing the chiral global symmetry, with a bifundamental field playing the role of the chiral condensate. We show that these expectations are born out in several supersymmetric examples. To analyze most of these properties it is not necessary to go beyond the probe limit in which one neglects the backreaction of the flavor D-branes.
1,052 citations
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TL;DR: In this paper, an economical theory of natural electroweak symmetry breaking was proposed, which stabilizes the electroweak scale with a naturally light Higgs and weakly coupled new physics at TeV energies.
Abstract: We present an economical theory of natural electroweak symmetry breaking, generalizing an approach based on deconstruction. This theory is the smallest extension of the Standard Model to date that stabilizes the electroweak scale with a naturally light Higgs and weakly coupled new physics at TeV energies. The Higgs is one of a set of pseudo Goldstone bosons in an SU(5)/SO(5) nonlinear sigma model. The symmetry breaking scale f is around a TeV, with the cutoff Λ4πf ~ 10 TeV. A single electroweak doublet, the `little Higgs', is automatically much lighter than the other pseudo Goldstone bosons. The quartic self-coupling for the little Higgs is generated by the gauge and Yukawa interactions with a natural size (g2, λt2), while the top Yukawa coupling generates a negative mass squared triggering electroweak symmetry breaking. Beneath the TeV scale the effective theory is simply the minimal Standard Model. The new particle content at TeV energies consists of one set of spin one bosons with the same quantum numbers as the electroweak gauge bosons, an electroweak singlet quark with charge 2/3, and an electroweak triplet scalar. One loop quadratically divergent corrections to the Higgs mass are cancelled by interactions with these additional particles.
1,004 citations
TL;DR: In this paper, the authors present a maximally supersymmetric IIB string background with a conformally flat lorentzian symmetric space G/K with solvable G, with a homogeneous five-form flux.
Abstract: We present a maximally supersymmetric IIB string background. The geometry is that of a conformally flat lorentzian symmetric space G/K with solvable G, with a homogeneous five-form flux. We give the explicit supergravity solution, compute the isometries, the 32 Killing spinors, and the symmetry superalgebra, and then discuss T-duality and the relation to M-theory.
822 citations
TL;DR: In this paper, the authors developed semiclassical quantization of superstring in a large circle of S^5, and derived the corresponding quadratic fluctuation action for bosonic and fermionic fields from the GS string action and computed the string 1-loop correction to the classical energy spectrum in the S,J sector.
Abstract: Motivated by recent proposals in hep-th/0202021 and hep-th/0204051 we develop semiclassical quantization of superstring in $AdS_5 x S^5$. We start with a classical solution describing string rotating in $AdS_5$ and boosted along large circle of $S^5$. The energy of the classical solution $E$ is a function of the spin $S$ and the momentum $J$ (R-charge) which interpolates between the limiting cases S=0 and J=0 considered previously. We derive the corresponding quadratic fluctuation action for bosonic and fermionic fields from the GS string action and compute the string 1-loop (large $\lambda= {R^4\over \a'^2}$) correction to the classical energy spectrum in the $(S,J)$ sector. We find that the 1-loop correction to the ground-state energy does not cancel for non-zero $S$. For large $S$ it scales as $\ln S$, i.e. as the classical term, with no higher powers of $\ln S$ appearing. This supports the conjecture made in hep-th/0204051 that the classical $E-S = a \ln S$ scaling can be interpolated to weak coupling to reproduce the corresponding operator anomalous dimension behaviour in gauge theory.
737 citations
TL;DR: In this article, the authors presented the minimal theory space model of electroweak symmetry breaking, with two sites and four link fields, and the minimal set of fermions, which is the first alternative to weak-scale supersymmetry with naturally light Higgs fields.
Abstract: Recently a new class of theories of electroweak symmetry breaking have been constructed. These models, based on deconstruction and the physics of theory space, provide the first alternative to weak-scale supersymmetry with naturally light Higgs fields and perturbative new physics at the TeV scale. The Higgs is light because it is a pseudo-Goldstone boson, and the quadratically divergent contributions to the Higgs mass are cancelled by new TeV scale ``partners'' of the same statistics. In this paper we present the minimal theory space model of electroweak symmetry breaking, with two sites and four link fields, and the minimal set of fermions. There are very few parameters and degrees of freedom beyond the Standard Model. Below a TeV, we have the Standard Model with two light Higgs doublets, and an additional complex scalar weak triplet and singlet. At the TeV scale, the new particles that cancel the 1-loop quadratic divergences in the Higgs mass are revealed. The entire Higgs potential needed for electroweak symmetry breaking - the quartic couplings as well as the familiar negative mass squared - can be generated by the top Yukawa coupling, providing a novel link between the physics of flavor and electroweak symmetry breaking.
612 citations
Journal Article•
TL;DR: In this article, the spinorial cohomology of ten-dimensional abelian SYM at order alpha'^3 was computed and it was shown that linear supersymmetry alone excludes the presence of alpha'+3-order corrections.
Abstract: We compute the spinorial cohomology of ten-dimensional abelian SYM at order alpha'^3 and we find that it is trivial. Consequently, linear supersymmetry alone excludes the presence of alpha'^3-order corrections. Our result lends support to the conjecture that there may be a unique supersymmetric deformation of ordinary ten-dimensional abelian SYM.
TL;DR: In this paper, the location of the critical point (E) in QCD with nf = 2+1 dynamical staggered quarks with semi-realistic masses on Lt = 4 lattices was determined.
Abstract: Based on universal arguments it is believed that there is a critical point (E) in QCD on the temperature (T) versus chemical potential (μ) plane, which is of extreme importance for heavy-ion experiments. Using finite size scaling and a recently proposed lattice method to study QCD at finite μ we determine the location of E in QCD with nf = 2+1 dynamical staggered quarks with semi-realistic masses on Lt = 4 lattices. Our result is TE = 160±3.5 MeV and μE = 725±35 MeV. For the critical temperature at μ = 0 we obtained Tc = 172±3 MeV.
TL;DR: In this article, the authors consider the dynamics of anti-D3 branes inside the Klebanov-Strassler geometry, the deformed conifold with M units of RR 3-form flux around the S3, and find that for p << M the system relaxes to a nonsupersymmetric NS 5-brane ''giant graviton' configuration, which is classically stable, but quantum mechanically can tunnel to a nearby supersymmetric vacuum with M−p D3 brane.
Abstract: We consider the dynamics of p anti-D3 branes inside the Klebanov-Strassler geometry, the deformed conifold with M units of RR 3-form flux around the S3. We find that for p << M the system relaxes to a nonsupersymmetric NS 5-brane `giant graviton' configuration, which is classically stable, but quantum mechanically can tunnel to a nearby supersymmetric vacuum with M−p D3 branes. This decay mode is exponentially suppressed and proceeds via the nucleation of an NS 5-brane bubble wall. We propose a dual field theory interpretation of the decay as the transition between a nonsupersymmetric `baryonic' branch and a supersymmetric `mesonic' branch of the corresponding SU(2M−p) × SU(M−p) low energy gauge theory. The NS 5-brane tunneling process also provides a simple visualization of the geometric transition by which D3-branes can dissolve into 3-form flux.
TL;DR: In this article, the chiral ring structure in a supersymmetric U(N) gauge theory with an adjoint chiral superfield and an arbitrary superpotential was studied.
Abstract: Motivated by recent work of Dijkgraaf and Vafa, we study anomalies and the chiral ring structure in a supersymmetric U(N) gauge theory with an adjoint chiral superfield and an arbitrary superpotential. A certain generalization of the Konishi anomaly leads to an equation which is identical to the loop equation of a bosonic matrix model. This allows us to solve for the expectation values of the chiral operators as functions of a finite number of ``integration constants.'' From this, we can derive the Dijkgraaf-Vafa relation of the effective superpotential to a matrix model. Some of our results are applicable to more general theories. For example, we determine the classical relations and quantum deformations of the chiral ring of = 1 super Yang-Mills theory with SU(N) gauge group, showing, as one consequence, that all supersymmetric vacua of this theory have a nonzero chiral condensate.
TL;DR: In this paper, the authors obtained the vacuum solutions for M-theory compactified on eight-manifolds with non-vanishing four-form flux by analyzing the scalar potential appearing in the three-dimensional theory.
Abstract: We obtain the vacuum solutions for M-theory compactified on eight-manifolds with non-vanishing four-form flux by analyzing the scalar potential appearing in the three-dimensional theory. Many of these vacua are not supersymmetric and yet have a vanishing three-dimensional cosmological constant.We show that in the context of type-IIB compactifications on Calabi-Yau threefolds with fluxes and external brane sources α'-corrections generate a correction to the supergravity potential proportional to the Euler number of the internal manifold which spoils the no-scale structure appearing in the classical potential. This indicates that α'-corrections may indeed lead to a stabilization of the radial modulus appearing in these compactifications.
TL;DR: In this paper, the leading-order hard photon emission rate in ultra-relativistic plasmas was derived using diagrammatic methods and extended to the case of gluon radiation.
Abstract: We recently derived, using diagrammatic methods, the leading-order hard photon emission rate in ultra-relativistic plasmas This requires a correct treatment of multiple scattering effects which limit the coherence length of emitted radiation (the Landau-Pomeranchuk-Migdal effect) In this paper, we provide a more physical derivation of this result, and extend the treatment to the case of gluon radiation
TL;DR: Giant gravitons in AdS5? S5, and its orbifolds, have a dual field theory representation as states created by chiral primary operators as discussed by the authors.
Abstract: Giant gravitons in AdS5 ? S5, and its orbifolds, have a dual field theory representation as states created by chiral primary operators. We argue that these operators are not single-trace operators in the conformal field theory, but rather are determinants and subdeterminants of scalar fields; the stringy exclusion principle applies to these operators. Evidence for this identification comes from three sources: (a) topological considerations in orbifolds, (b) computation of protected correlators using free field theory and (c) a Matrix model argument. The last argument applies to AdS7 ? S4 and the dual (2,0) theory, where we use algebraic aspects of the fuzzy 4-sphere to compute the expectation value of a giant graviton operator along the Coulomb branch of the theory.
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TL;DR: In this paper, it was shown that S-branes arise in string theory as time-dependent solutions of the world volume tachyon field of an unstable D-brane or D-Brane-anti-D-braine pair.
Abstract: Scalar field theories with appropriate potentials in Minkowski space can have time-dependent classical solutions containing topological defects which correspond to S-branes - i.e. branes all of whose tangential dimensions are spacelike. It is argued that such S-branes arise in string theory as time-dependent solutions of the worldvolume tachyon field of an unstable D-brane or D-brane-anti-D-brane pair. Using the known coupling of the spacetime RR fields to the worldvolume tachyon it is shown that these S-branes carry a charge, defined as the integral of a RR field strength over a sphere (containing a time as well as spatial dimensions) surrounding the S-brane. This same charge is carried by SD-branes, i.e. Dirichlet branes arising from open string worldsheet conformal field theories with a Dirichlet boundary condition on the timelike dimension. The corresponding SD-brane boundary state is constructed. Supergravity solutions carrying the same charges are also found for a few cases.
TL;DR: In this paper, the authors show how quiver quantum mechanics smoothly interpolates between the two, and use this, together with recent mathematical results on the cohomology of quiver varieties, to solve some nontrivial ground state counting problems in multi-particle quantum mechanics, including one arising in the setup of the spherical quantum Hall effect.
Abstract: Two pictures of BPS bound states in Calabi-Yau compactifications of type II string theory exist, one as a set of particles at equilibrium separations from each other, the other as a fusion of D-branes at a single point of space. We show how quiver quantum mechanics smoothly interpolates between the two, and use this, together with recent mathematical results on the cohomology of quiver varieties, to solve some nontrivial ground state counting problems in multi-particle quantum mechanics, including one arising in the setup of the spherical quantum Hall effect, and to count ground state degeneracies of certain dyons in supersymmetric Yang-Mills theories. A crucial ingredient is a non-renormalization theorem in N = 4 quantum mechanics for the first order part of the Lagrangian in an expansion in powers of velocity.
TL;DR: In this article, the authors used a near-extremal black brane background to compute the retarded Green's functions of the stress-energy tensor in = 4 super-Yang-Mills (SYM) theory at finite temperature.
Abstract: As a non-trivial check of the non-supersymmetric gauge/gravity duality, we use a near-extremal black brane background to compute the retarded Green's functions of the stress-energy tensor in = 4 super-Yang-Mills (SYM) theory at finite temperature. For the long-distance, low-frequency modes of the diagonal components of the stress-energy tensor, hydrodynamics predicts the existence of a pole in the correlators corresponding to propagation of sound waves in the = 4 SYM plasma. The retarded Green's functions obtained from gravity do indeed exhibit this pole, with the correct values for the sound speed and the rate of attenuation.
TL;DR: In this paper, the authors consider the implications of a cosmological constant for the evolution of the universe, under a set of assumptions motivated by the holographic and horizon complementarity principles.
Abstract: In this paper we consider the implications of a cosmological constant for the evolution of the universe, under a set of assumptions motivated by the holographic and horizon complementarity principles. We discuss the ``causal patch'' description of spacetime required by this framework, and present some simple examples of cosmologies described this way. We argue that these assumptions inevitably lead to very deep paradoxes, which seem to require major revisions of our usual assumptions.
TL;DR: In this paper, the authors study conformal field theories in two dimensions separated by domain walls, which preserve at least one Virasoro algebra, and show that the Casimir energy between a wall and an anti-wall can be computed as the classical energy of a brane that connects the walls.
Abstract: We study conformal field theories in two dimensions separated by domain walls, which preserve at least one Virasoro algebra. We develop tools to study such domain walls, extending and clarifying the concept of `folding' discussed in the condensed-matter literature. We analyze the conditions for unbroken supersymmetry, and discuss the holographic duals in AdS3 when they exist. One of the interesting observables is the Casimir energy between a wall and an anti-wall. When these separate free scalar field theories with different target-space radii, the Casimir energy is given by the dilogarithm function of the reflection probability. The walls with holographic duals in AdS3 separate two sigma models, whose target spaces are moduli spaces of Yang-Mills instantons on T4 or K3. In the supergravity limit, the Casimir energy is computable as classical energy of a brane that connects the walls through AdS3. We compare this result with expectations from the sigma-model point of view.
TL;DR: In this article, a duality between Yang-Mills theory with large R-charge J and string theory in a pp-wave background has been proposed, and the genus counting parameter is shown to be g2(?')1/2 for a wide class of excited string states propagating on the ppwave background.
Abstract: Recently, Berenstein et al. have proposed a duality between a sector of = 4 super-Yang-Mills theory with large R-charge J, and string theory in a pp-wave background. In the limit considered, the effective 't Hooft coupling has been argued to be ?' = gYM2N/J2 = 1/(?p+?')2. We study Yang-Mills theory at small ?' (large ?) with a view to reproducing string interactions. We demonstrate that the effective genus counting parameter of the Yang-Mills theory is g22 = J4/N2 = (4?gs)2(?p+?')4, the effective two-dimensional Newton constant for strings propagating on the pp-wave background. We identify g2(?')1/2 as the effective coupling between a wide class of excited string states on the pp-wave background. We compute the anomalous dimensions of BMN operators at first order in g22 and ?' and interpret our result as the genus one mass renormalization of the corresponding string state. We postulate a relation between the three-string vertex function and the gauge theory three-point function and compare our proposal to string field theory. We utilize this proposal, together with quantum mechanical perturbation theory, to recompute the genus one energy shift of string states, and find precise agreement with our gauge theory computation.
TL;DR: In this article, the supersymmetric D-brane embeddings in the pp-wave background were shown to be super-symmetric by showing that the kappa symmetry projections are compatible with half of the target space.
Abstract: We find half supersymmetric AdS-embeddings in AdS_5 x S^5 corresponding to all quarter BPS orthogonal intersections of D3-branes with Dp-branes. A particular case is the Karch-Randall embedding AdS_4 x S^2. We explicitly prove that these embeddings are supersymmetric by showing that the kappa symmetry projections are compatible with half of the target space Killing spinors and argue that all these cases lead to AdS/dCFT dualities involving a CFT with a defect. We also find an asymptotically AdS_4 x S^2 embedding that corresponds to a holographic RG-flow on the defect. We then consider the pp-wave limit of the supersymmetric AdS-embeddings and show how it leads to half supersymmetric D-brane embeddings in the pp-wave background. We systematically analyze D-brane embeddings in the pp-wave background along with their supersymmetry. We construct all supersymmetric D-branes wrapped along the light-cone using operators in the dual gauge theory: the open string states are constructed using defect fields. We also find supersymmetric D1 (monopoles) and D3 (giant gravitons) branes that wrap only one of the light-cone directions. These correspond to non-perturbative states in the dual gauge theory.
TL;DR: In this article, the authors point out the existence of nonlinear σ-models on group manifolds which are left symmetric and right Poisson-Lie symmetric, and discuss the corresponding rich T-duality story with particular emphasis on two examples: the anisotropic principal chiral model and the SL(2,)/SU(2) WZW model.
Abstract: We point out the existence of nonlinear σ-models on group manifolds which are left symmetric and right Poisson-Lie symmetric. We discuss the corresponding rich T-duality story with particular emphasis on two examples: the anisotropic principal chiral model and the SL(2,)/SU(2) WZW model. The latter has the de Sitter space as its (conformal) non-abelian dual.
TL;DR: In this paper, the charge group for symmetry preserving D-branes on group manifolds for simple, simply-connected, connected compact Lie groups G has been computed, where G is a Lie group.
Abstract: In this paper we compute the charge group for symmetry preserving D-branes on group manifolds for all simple, simply-connected, connected compact Lie groups G.
TL;DR: In this paper, an algorithm is presented in which the colour-dipole Cascade Model as implemented in the Ariadne program is corrected to match the fixed order tree-level matrix elements for e e(+) --> n jets.
Abstract: An algorithm is presented in which the Colour-Dipole Cascade Model as implemented in the Ariadne program is corrected to match the fixed order tree-level matrix elements for e e(+) --> n jets. The result is a full parton level generator for e e(+) annihilation where the generated states are correct on tree-level to fixed order in alpha(s) and to all orders with modified leading logarithmic (MLLA) accuracy. In this paper, matrix elements are used up to second order in alpha(s), but the scheme is applicable also for higher orders. A strategy for also including exact virtual corrections to fixed order is suggested and the possibility to extend the scheme to hadronic collisions is discussed.
TL;DR: In this paper, a supersymmetric extension of the standard MSSM was introduced, in which the gauge sector contains complete N = 2 supersymmetry multiplets, and the resulting squark and slepton masses are finite, calculable, positive and flavor universal.
Abstract: We introduce a new supersymmetric extension of the standard model in which the gauge sector contains complete N = 2 supersymmetry multiplets. Supersymmetry breaking from the D-term vev of a hidden sector U(1) gauge field leads to Dirac soft supersymmetry breaking gaugino masses, and a new type of soft scalar trilinear couplings. The resulting squark and slepton masses are finite, calculable, positive and flavor universal. The Higgs soft mass squared is negative. The phenomenology of these theories differs significantly from the MSSM. We discuss a variety of possible origins for the soft operators and new fields, including models in both four and higher dimensions.
TL;DR: AMEGIC++ as mentioned in this paper is a matrix element generator dedicated to describing multi-particle production in high energy particle collisions, which automatically generates helicity amplitudes for the processes under consideration and constructs suitable, efficient integration channels for the multi-channel phase space integration.
Abstract: The new matrix element generator AMEGIC++ is introduced, dedicated to describe multi-particle production in high energy particle collisions. It automatically generates helicity amplitudes for the processes under consideration and constructs suitable, efficient integration channels for the multi-channel phase space integration. The corresponding expressions for the amplitudes and the integrators are stored in library files to be linked to the main program.
TL;DR: In this paper, the authors constructed a series of four dimensional non-critical string theories with eight supercharges, dual to theories of light electric and magnetic charges, for which exact formulas for the central charge of the space-time supersymmetry algebra as a function of the world-sheet couplings were obtained.
Abstract: Recently, the author has constructed a series of four dimensional non-critical string theories with eight supercharges, dual to theories of light electric and magnetic charges, for which exact formulas for the central charge of the space-time supersymmetry algebra as a function of the world-sheet couplings were obtained. The basic idea was to generalize the old matrix model approach, replacing the simple matrix integrals by the four dimensional matrix path integrals of N=2 supersymmetric Yang-Mills theory, and the Kazakov critical points by the Argyres-Douglas critical points. In the present paper, we study qualitatively similar toy path integrals corresponding to the two dimensional N=2 supersymmetric non-linear sigma model with target space CP^n and twisted mass terms. This theory has some very strong similarities with N=2 super Yang-Mills, including the presence of critical points in the vicinity of which the large n expansion is IR divergent. The model being exactly solvable at large n, we can study non-BPS observables and give full proofs that double scaling limits exist and correspond to universal continuum limits. A complete characterization of the double scaled theories is given. We find evidence for dimensional transmutation of the string coupling in some non-critical string theories. We also identify en passant some non-BPS particles that become massless at the singularities in addition to the usual BPS states.