Showing papers on "Superpotential published in 2000"

Natural chaotic inflation in supergravity

Abstract: We propose a chaotic inflation model in supergravity. In the model the K\"ahler potential has a Nambu-Goldstone--type shift symmetry of the inflaton chiral multiplet which ensures the flatness of the inflaton potential beyond the Planck scale. We show that chaotic inflation naturally takes place by introducing a small breaking term of the shift symmetry in the superpotential. This may open a new branch of model building for inflationary cosmology in the framework of supergravity.

Gravity Duals of Supersymmetric SU(N) x SU(N+M) Gauge Theories

Abstract: The world volume theory on N regular and M fractional D3-branes at the conifold singularity is a non-conformal n=1 supersymmetric SU(N+M) x SU(N) gauge theory. In previous work the Type IIB supergravity dual of this theory was constructed to leading non-trivial order in M/N: it is the AdS_5 x T^{1,1} background with NS-NS and R-R 2-form fields turned on. Far in the UV this dual description was shown to reproduce the logarithmic flow of couplings found in the field theory. In this paper we study the supersymmetric RG flow at all scales. We introduce an ansatz for the 10-d metric and other fields and show that the equations of motion may be derived in first order form from a simple superpotential. This allows us to explicitly solve for the gravity dual of the RG trajectory.

Supersymmetric three-form flux perturbations on AdS 5

Abstract: We consider warped type IIB supergravity solutions with three-form flux and $\mathcal{N}=1$ supersymmetry, which arise as the supergravity duals of confining gauge theories We first work in a perturbation expansion around ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{5}$, as in the work of Polchinski and Strassler, and from the $\mathcal{N}=1$ conditions and the Bianchi identities recover their first-order solution generalized to an arbitrary $\mathcal{N}=1$ superpotential We find the second order dilaton and axion by the same means We also find a simple family of exact solutions, which can be obtained from solutions found by Becker and Becker, and which includes the recent Klebanov-Strassler solution

Open string instantons and superpotentials

Abstract: We study the F terms in $\mathcal{N}=1$ supersymmetric, $d=4$ gauge theories arising from $D(p+3)$-branes wrapping supersymmetric p-cycles in a Calabi-Yau threefold. If p is even the spectrum and superpotential for a single brane are determined by purely classical $({\ensuremath{\alpha}}^{\ensuremath{'}}\ensuremath{\rightarrow}0)$ considerations. If $p=3,$ superpotentials for massless modes are forbidden to all orders in ${\ensuremath{\alpha}}^{\ensuremath{'}}$ and may only be generated by open string instantons. For this latter case we find that such instanton effects are generically present. Mirror symmetry relates even and odd p and thus perturbative and nonperturbative superpotentials; we provide a preliminary discussion of a class of examples of such mirror pairs.

On the Vacuum Structure of Type II String Compactifications on Calabi-Yau Spaces with H-Fluxes

Abstract: We discuss the vacuum structure of type IIA/B Calabi-Yau string compactifications to four dimensions in the presence of n-form H-fluxes. These will lift the vacuum degeneracy in the Calabi-Yau moduli space, and for generic points in the moduli space, N=2 supersymmetry will be broken. However, for certain `aligned' choices of the H-flux vector, supersymmetric ground states are possible at the degeneration points of the Calabi-Yau geometry. We will investigate in detail the H-flux induced superpotential and the corresponding scalar potential at several degeneration points, such as the Calabi-Yau large volume limit, the conifold loci, the Seiberg-Witten points, the strong coupling point and the conformal points. Some emphasis is given to the question whether partial supersymmetry breaking can be realized at those points. We also relate the H-flux induced superpotential to the formalism of gauged N=2 supergravity. Finally we point out the analogies between the Calabi-Yau vacuum structure due to H-fluxes and the attractor formalism of N=2 black holes.

Supersymmetry In Quantum and Classical Mechanics

Abstract: GENERAL REMARKS ON SUPERSYMMETRY Background BASIC PRINCIPLES OF SUPERSYMMETRIC QUANTUM MECHANICS SUSY and the Oscillator Problem Superpotential and Setting Up a Supersymmetric Hamiltonian Physical Interpretation of Hs Properties of the Partner Hamiltonians Applications Superspace Formalism Other Schemes of SUSY SUPERSYMMETRIC CLASSICAL MECHANICS Classical Poisson Bracket, Its Generalizations Some Algebraic Properties of the Generalized Poisson Bracket A Classical Supersymmetric Model SUSY Breaking, Witten Index and Index Condition SUSY Breaking Witten Index Finite Temperature SUSY Regulated Witten Index Index Condition q-Deformation and Index Condition Parabosons Deformed Parabose States and Index Condition Witten's Index and Higher-Derivative SUSY Explicit SUSY Breaking and Singular Superpotentials FACTORIZATION METHOD, SHAPE INVARIANCE AND GENERATION OF SOLVABLE PROBLEMS Preliminary Remarks Factorization Method of Infeld and Hull Shape Invariance Condition Self-Similar Potentials A Note on the Generalized Quantum Condition Non-Uniqueness of the Factorizability Phase Equivalent Potentials Generation of Exactly Solvable Potentials in SUSYQM Conditionally Solvable Potentials and SUSY RADIAL PROBLEMS AND SPIN-ORBIT COUPLING SUSY and the Radial Problems Radial Problems Using Ladder Operator Techniques in SUSYQM Isotropic Oscillator and Spin-Orbit Coupling SUSY in D- Dimensions SUPERSYMMETRY IN NONLINEAR SYSTEMS The KdV Equation Conservation Laws in Nonlinear Systems Lax Equations SUSY and Conservation Laws in the KdV - MKdV Systems Darboux's Method SUSY and Conservation Laws in the KdV-SG Systems Supersymmetric KdV Conclusion PARASUPERSYMMETRY Introduction Models of PSUSYQM PSUSY of Arbitrary Order p Truncated Oscillator and PSUSYQM Multidimensional Parasuperalgebras APPENDIX Note: Each chapter also contains a References section

World-sheet corrections via D-instantons

Abstract: We use a D-instanton or physical gauge approach to re-derive the heterotic string worldsheet instanton contribution to the superpotential in Calabi-Yau compactification. We derive an analogous formula for worldsheet instanton corrections to the moduli space metric in heterotic string or type-I compactification on a K3 surface. In addition, we give a global analysis of the phase of the worldsheet path integral of the heterotic string, showing precisely how the B-field must be interpreted.

On Realising N=1 Super Yang-Mills in M theory

Abstract: Pure N=1 super Yang-Mills theory can be realised as a certain low energy limit of M theory near certain singularities in $G_2$-holonomy spaces For SU(n) and SO(2n) gauge groups these $M$ theory backgrounds can be regarded as strong coupling limits of wrapped D6-brane configurations in Type IIA theory on certain non-compact Calabi-Yau spaces such as the deformed conifold Various aspects of such realisations are studied including the generation of the superpotential, domain walls, QCD strings and the relation to recent work of Vafa In the spirit of this recent work we propose a `gravity dual' of M theory near these singularities

Complex geometry of conifolds and 5-brane wrapped on 2-sphere

Abstract: We investigate solutions of type II supergravity which have the product R^4 x M^6 structure with non-compact M^6 factor and which preserve at least four supersymmetries. In particular, we consider various conifolds and the N=1 supersymmetric NS5-brane wrapped on 2-sphere solution recently discussed in hep-th/0008001. In all of these cases, we explicitly construct the complex structures, and the Kaehler and parallel (3,0) forms of the corresponding M^6. In addition, we verify that the above solutions preserve, respectively, eight and four supersymmetries of type II theory. We also demonstrate that the ordinary and fractional D3-brane solutions on singular, resolved and deformed conifolds, and the (S-dual of) NS5-brane wrapped on 2-sphere can be obtained as special cases from a universal ansatz for the supergravity fields and a single 1-d action governing their radial evolution. We show that like the 3-branes on conifolds, the NS5-brane on 2-sphere background can be found as a solution of first order system following from a superpotential.

Radius Stabilization and Anomaly-Mediated Supersymmetry Breaking

Abstract: We analyze in detail a specific 5-dimensional realization of a ``brane-universe'' scenario where the visible and hidden sectors are localized on spatially separated 3-branes coupled only by supergravity, with supersymmetry breaking originating in the hidden sector. Although general power counting allows order ${1/M}_{\mathrm{Planck}}^{2}$ contact terms between the two sectors in the 4-dimensional theory from exchange of supergravity Kaluza-Klein modes, we show that they are not present by carefully matching to the 5-dimensional theory. We also find that the radius modulus corresponding to the size of the compactified dimension must be stabilized by additional dynamics in order to avoid runaway behavior after supersymmetry breaking and to understand the communication of supersymmetry breaking. We stabilize the radius by adding two pure Yang-Mills sectors, one in the bulk and the other localized on a brane. Gaugino condensation in the 4-dimensional effective theory generates a superpotential that can naturally fix the radius at a sufficiently large value that supersymmetry breaking is communicated dominantly by the recently discovered mechanism of anomaly mediation. The mass of the radius modulus is large compared to ${m}_{3/2}.$ The stabilization mechanism requires only parameters of order one at the fundamental scale, with no fine-tuning except for the cosmological constant.

Supersymmetry and the brane world

Abstract: We investigate the possibility of gravity localization on the brane in the context of supersymmetric theories. To realize this scenario one needs to find a theory with the supersymmetric flow stable in IR at two critical points, one with positive and the other with negative values of the superpotential. We perform a general study of the supersymmetric flow equations of gauged massless supergravity interacting with arbitrary number of vector multiplets and demonstrate that localization of gravity does not occur. The same conclusion remains true when tensor multiplets are included. We analyze all recent attempts to find a BPS brane-world and conclude that localization of gravity on the brane in supersymmetric theories remains a challenging but unsolved problem.

Inflation and monopoles in supersymmetric SU(4)c × SU(2)L × SU(2)R

Abstract: We show how hybrid inflation can be successfully realized in a supersymmetric model with gauge group GPS = SU(4)c ? SU(2)L ? SU(2)R. By including a non-renormalizable superpotential term, we generate an inflationary valley along which GPS is broken to the standard model gauge group. Thus, catastrophic production of the doubly charged magnetic monopoles, which are predicted by the model, cannot occur at the end of inflation. The results of the cosmic background explorer can be reproduced with natural values (of order 10?3) of the relevant coupling constant, and symmetry breaking scale of GPS of the order of 1016 GeV. The spectral index of density perturbations lies between unity and 0.9. Moreover, the ?-term is generated via a Peccei-Quinn symmetry and proton is practically stable. Baryogenesis in the universe takes place via leptogenesis. The low deuterium abundance constraint on the baryon asymmetry, the gravitino limit on the reheat temperature and the requirement of almost maximal ????? mixing from SUPER-KAMIOKANDE can be simultaneously met with m??, m?? and heaviest Dirac neutrino mass determined from the large angle MSW resolution of the solar neutrino problem, the SUPER-KAMIOKANDE results and SU(4)c symmetry respectively.

Anti-de Sitter vacua of gauged supergravities with 8 supercharges

Abstract: We investigate supersymmetric extrema of Abelian gauged supergravity theories with nontrivial vector multiplets and 8 supercharges in four and five dimensions. The scalar fields of these models parametrize a manifold consisting of disconnected branches and, restricting to the case where this manifold has a nonsingular metric, we show that on every branch there can be at most one extremum, which is a local maximum (for W>0) or a minimum (for W<0) of the superpotential W. Therefore, these supergravity models do not allow for regular domain wall solutions interpolating between different extrema of the superpotential and the space-time transverse to the wall asymptotically always approaches the boundary of AdS (UV-fixed points in a dual field theory). (c) 2000 The American Physical Society.

Currents and superpotentials in classical gauge theories: II. Global aspects and the example of affine gravity

Abstract: The conserved charges associated to gauge symmetries are defined at a boundary component of space-time because the corresponding Noether current can be rewritten on-shell as the divergence of a superpotential. However, the latter is afflicted by ambiguities. Regge and Teitelboim found a procedure to lift the arbitrariness in the Hamiltonian framework. An alternative covariant formula was proposed by one of us for an arbitrary variation of the superpotential, it depends only on the equations of motion and on the gauge symmetry under consideration. Here we emphasize that in order to compute the charges, it is enough to stay at a boundary of spacetime, without requiring any hypothesis about the bulk or about other boundary components, so one may speak of holographic charges. It is well known that the asymptotic symmetries that lead to conserved charges are really defined at infinity, but the choice of boundary conditions and surface terms in the action and in the charges is usually determined through integration by parts whereas each component of the boundary should be considered separately. We treat the example of gravity (for any space-time dimension, with or without cosmological constant), formulated as an Affine theory which is a natural generalization of the Palatini and Cartan-Weyl (vielbein) first order formulations. We then show that the superpotential associated to a Dirichlet boundary condition on the metric (the one needed to treat asymptotically flat or

On the Landau-Ginzburg description of boundary CFTs and special Lagrangian submanifolds

Abstract: We consider Landau-Ginzburg (LG) models with boundary conditions pre- serving A-type N = 2 supersymmetry. We show the equivalence of a linear class of boundary conditions in the LG model to a particular class of boundary states in the cor- responding CFT by an explicit computation of the open-string Witten index in the LG model. We extend the linear class of boundary conditions to general non-linear bound- ary conditions and determine their consistency with A-type N = 2 supersymmetry. This enables us to provide a microscopic description of special Lagrangian submani- folds in C n due to Harvey and Lawson. We generalise this construction to the case of hypersurfaces in P n . We nd that the boundary conditions must necessarily have vanishing Poisson bracket with the combination (W () W ()), where W ( )i s the appropriate superpotential for the hypersurface. An interesting application considered is the T 3 supersymmetric cycle of the quintic in the large complex structure limit.

Flux, Supersymmetry and M theory on 7-manifolds

Abstract: Various aspects of low energy M theory compactified to four dimensions are considered. If the supersymmetry parameter is parallel in the unwarped metric, then supersymmetry requires that the warp factor is trivial, the background four-form field strength is zero and that the internal 7-manifold has $G_2$ holonomy (we assume the absence of boundaries and other impurities). A proposal of Gukov - extended here to include M2-brane domain walls - for the superpotential of the compactified theory is shown to yield the same result. Finally, we make some speculative remarks concerning higher derivative corrections and supersymmetry breaking.

A Symplectic Hamiltonian derivation of quasilocal energy momentum for GR

Abstract: The various roles of boundary terms in the gravitational Lagrangian and Hamiltonian are explored. A symplectic Hamiltonian-boundary-term approach is ideally suited for a large class of quasilocal energy-momentum expressions for general relativity. This approach provides a physical interpretation for many of the well-known gravitational energy-momentum expressions including all of the pseudotensors, associating each with unique boundary conditions. From this perspective we find that the pseudotensors of Einstein and M{\o}ller (which is closely related to Komar's superpotential) are especially natural, but the latter has certain shortcomings. Among the infinite possibilities, we found that there are really only two Hamiltonian-boundary-term quasilocal expressions which correspond to {\em covariant} boundary conditions; they are respectively of the Dirichlet or Neumann type. Our Dirichlet expression coincides with the expression recently obtained by Katz and coworkers using Noether arguments and a fixed background. A modification of their argument yields our Neumann expression.

Quantum cosmology and open universes

Abstract: The quantum creation of universes with compact spacelike sections that have curvature k either closed, flat, or open, i.e., $k=\ifmmode\pm\else\textpm\fi{}1,0,$ is studied. In the flat and open cases, the superpotential of the Wheeler-DeWitt equation is significantly modified, and as a result the qualitative behavior of a typical wave function differs from the traditional closed case. In the open case boundary conditions that include the tunneling ones are allowed but not the no-boundary choice. Restricting ourselves to the tunneling boundary condition, and applying it in turn to each of these curvatures, it is shown that quantum cosmology actually suggests that the universe is open, $k=\ensuremath{-}1.$ In all cases sufficient inflation $\ensuremath{\sim}60$ e foldings are predicted: this is an improvement over classical measures that generally are ambiguous as to whether inflation is certain to occur.

Supersymmetric Spin Networks and Quantum Supergravity

Abstract: We define supersymmetric spin networks, which provide a complete set of gauge invariant states for supergravity and supersymmetric gauge theories. The particular case of Osp(1|2) is studied in detail and applied to the non-perturbative quantization of supergravity. The supersymmetric extension of the area operator is defined and partly diagonalized. The spectrum is discrete as in quantum general relativity, and the two cases could be distinguished by measurements of quantum geometry.

A Symplectic Hamiltonian Derivation of Quasilocal Energy-Momentum for GR

Abstract: The various roles of boundary terms in the gravitational Lagrangian and Hamiltonian are explored. A symplectic Hamiltonian-boundary-term approach is ideally suited for a large class of quasilocal energy-momentum expressions for general relativity. This approach provides a physical interpretation for many of the well-known gravitational energy-momentum expressions including all of the pseudotensors, associating each with unique boundary conditions. From this perspective we find that the pseudotensors of Einstein and M{\o}ller (which is closely related to Komar's superpotential) are especially natural, but the latter has certain shortcomings. Among the infinite possibilities, we found that there are really only two Hamiltonian-boundary-term quasilocal expressions which correspond to {\em covariant} boundary conditions; they are respectively of the Dirichlet or Neumann type. Our Dirichlet expression coincides with the expression recently obtained by Katz and coworkers using Noether arguments and a fixed background. A modification of their argument yields our Neumann expression.

Reheating and Supersymmetric Flat-Direction Baryogenesis

Abstract: We re-examine Affleck-Dine baryo/leptogenesis from the oscillation of condensates along flat directions of the supersymmetric standard model, which attained large vevs at the end of inflationary epoque. The key observation is that superpotential interactions couple the flat directions to other fields, which acquire masses induced by the flat-direction vev that may be sufficiently small for them to be kinematically accessible to inflaton decay. The resulting plasma of inflaton decay products then may act on the flat directions via these superpotential Yukawa couplings, inducing thermal masses and supersymmetry-breaking A terms. In such cases the flat directions start their oscillations at an earlier time than usually estimated. The oscillations are also terminated earlier, due to evaporation of the flat direction condensate produced by its interaction with the plasma of inflaton decay products. In these cases we find that estimates for the resulting baryon/lepton asymmetry of the universe are substantially altered. We identify scenarios for the Yukawa couplings to the flat directions, and the order and mass scale of higher-dimensional superpotential interactions that set the initial flat direction vev, that might lead to acceptable baryo/leptogenesis.

A Study of holographic renormalization group flows in D = 6 and D = 3

Abstract: We present an explicit study of the holographic renormalization group (RG) in six dimensions using minimal gauged supergravity. By perturbing the theory with the addition of a relevant operator of dimension four one flows to a non-supersymmetric conformal fixed point. There are also solutions describing non-conformal vacua of the same theory obtained by giving an expectation value to the operator. One such vacuum is supersymmetric and is obtained by using the true superpotential of the theory. We discuss the physical acceptability of these vacua by applying the criteria recently given by Gubser for the four-dimensional case and find that those criteria give a clear physical picture in the six-dimensional case as well. We use this example to comment on the role of the Hamilton-Jacobi equations in implementing the RG. We conclude with some remarks on AdS4 and the status of three-dimensional superconformal theories from squashed solutions of M-theory.