Showing papers on "Partition function (quantum field theory) published in 2006"
TL;DR: In this paper, a formula for the exact partition function of 1/4 BPS dyons in a class of CHL models has been proposed, which involves inverse of Siegel modular forms of subgroups of Sp(2,).
Abstract: A formula for the exact partition function of 1/4 BPS dyons in a class of CHL models has been proposed earlier. The formula involves inverse of Siegel modular forms of subgroups of Sp(2,). In this paper we propose product formulae for these modular forms. This generalizes the result of Borcherds and Gritsenko and Nikulin for the weight 10 cusp form of the full Sp(2,) group.
184 citations
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TL;DR: In this paper, the authors revisited the self-dual field theory in 4l+2 dimensions using Chern-Simons theory in fourl+3 dimensions, building on the work of Witten.
Abstract: We revisit the construction of self-dual field theory in 4l+2 dimensions using Chern-Simons theory in 4l+3 dimensions, building on the work of Witten. Careful quantization of the Chern-Simons theory reveals all the topological subtleties associated with the self-dual partition function, including the generalization of the choice of spin structure needed to define the theory. We write the partition function for arbitrary torsion background charge, and in the presence of sources. We show how this approach leads to the formulation of an action principle for the self-dual field.
156 citations
TL;DR: In this paper, the integrand in the bosonic functional integral is defined only up to a phase without an additional choice, and the choice is referred to as "setting the quantum integrand".
Abstract: In anomaly-free quantum field theories the integrand in the bosonic functional integral—the exponential of the effective action after integrating out fermions—is often defined only up to a phase without an additional choice. We term this choice ``setting the quantum integrand''. In the low-energy approximation to M-theory the E
8-model for the C-field allows us to set the quantum integrand using geometric index theory. We derive mathematical results of independent interest about pfaffians of Dirac operators in 8k+3 dimensions, both on closed manifolds and manifolds with boundary. These theorems are used to set the quantum integrand of M-theory for closed manifolds and for compact manifolds with either temporal (global) or spatial (local) boundary conditions. In particular, we show that M-theory makes sense on arbitrary 11-manifolds with spatial boundary, generalizing the construction of heterotic M-theory on cylinders.
121 citations
TL;DR: In this paper, a generalisation of the core to coalitional games with externalities is presented, where the value of a deviation is given by an endogenous response, the solution of the residual game.
Abstract: We present a well-defined generalisation of the core to coalitional games with externalities, where the value of a deviation is given by an endogenous response, the solution (if nonempty: the core) of the residual game.
112 citations
TL;DR: In this paper, a relation between 4D and 5D black holes was used to derive exact BPS black hole degeneracies for 4D = 8 string theory from exactly known 5D degeneracies.
Abstract: A recently discovered relation between 4D and 5D black holes is used to derive exact (weighted) BPS black hole degeneracies for 4D = 8 string theory from the exactly known 5D degeneracies. A direct 4D microscopic derivation in terms of weighted 4D D-brane bound state degeneracies is sketched and found to agree.
88 citations
TL;DR: In this paper, a quantum statistical mechanical system which generalizes the Bost-Connes system to imaginary quadratic fields K of arbitrary class number and fully incorporates the explicit class field theory for such fields was constructed.
Abstract: We construct a quantum statistical mechanical system which generalizes the Bost–Connes system to imaginary quadratic fields K of arbitrary class number and fully incorporates the explicit class field theory for such fields. This system admits the Dedekind zeta function as partition function and the idele class group as group of symmetries. The extremal KMS states at zero temperature intertwine this symmetry with the Galois action on the values of the states on the arithmetic subalgebra. The geometric notion underlying the construction is that of commensurability of K-lattices.
79 citations
TL;DR: In this paper, the authors established a correspondence between polynomial representations of the Temperley and Lieb algebra and certain deformations of the Quantum Hall Effect wave functions, and gave a proof of the identification of the sum of the entries of the O(n) transfer matrix and a six vertex-model partition function, alternative to that of P. Di Francesco and P. Zinn-Justin.
Abstract: We establish a correspondence between polynomial representations of the Temperley and Lieb algebra and certain deformations of the Quantum Hall Effect wave functions. When the deformation parameter is a third root of unity, the representation degenerates and the wave functions coincide with the domain wall boundary condition partition function appearing in the conjecture of A.V. Razumov and Y.G. Stroganov. In particular, this gives a proof of the identification of the sum of the entries of the O(n) transfer matrix and a six vertex-model partition function, alternative to that of P. Di Francesco and P. Zinn-Justin.
75 citations
TL;DR: The Bayesian inference approach appears to be promising in this context of prediction of RNA secondary structure, and the performance of thermodynamics-based methods is limited by thermodynamic rules and parameters.
Abstract: Prediction of RNA secondary structure is a fundamental problem in computational structural biology. For several decades, free energy minimization has been the most popular method for prediction from a single sequence. In recent years, the McCaskill algorithm for computation of partition function and base-pair probabilities has become increasingly appreciated. This paradigm-shifting work has inspired the developments of extended partition function algorithms, statistical sampling and clustering, and application of Bayesian statistical inference. The performance of thermodynamics-based methods is limited by thermodynamic rules and parameters. However, further improvements may come from statistical estimates derived from structural databases for thermodynamics parameters with weak or little experimental data. The Bayesian inference approach appears to be promising in this context.
72 citations
Proceedings Article•
04 Dec 2006TL;DR: This work base the approximation on a different tractable model, planar graphs with binary variables and pure interaction potentials (no external field), and shows how such tractable planar models can be used in a decomposition to derive upper bounds on the partition function of non-planar models.
Abstract: A number of exact and approximate methods are available for inference calculations in graphical models. Many recent approximate methods for graphs with cycles are based on tractable algorithms for tree structured graphs. Here we base the approximation on a different tractable model, planar graphs with binary variables and pure interaction potentials (no external field). The partition function for such models can be calculated exactly using an algorithm introduced by Fisher and Kasteleyn in the 1960s. We show how such tractable planar models can be used in a decomposition to derive upper bounds on the partition function of non-planar models. The resulting algorithm also allows for the estimation of marginals. We compare our planar decomposition to the tree decomposition method of Wain-wright et. al., showing that it results in a much tighter bound on the partition function, improved pairwise marginals, and comparable singleton marginals.
62 citations
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TL;DR: In this article, the authors study the holomorphic Euler characteristics of determinant line bundles on moduli spaces of rank 2 semistable sheaves on an algebraic surface X, which can be viewed as $K$-theoretic versions of the Donaldson invariants.
Abstract: In this paper we study the holomorphic Euler characteristics of determinant line bundles on moduli spaces of rank 2 semistable sheaves on an algebraic surface X, which can be viewed as $K$-theoretic versions of the Donaldson invariants. In particular, if X is a smooth projective toric surface, we determine these invariants and their wallcrossing in terms of the K-theoretic version of the Nekrasov partition function (called 5-dimensional supersymmetric Yang-Mills theory compactified on a circle in the physics literature). Using the results of math.AG/0606180 we give an explicit generating function for the wallcrossing of these invariants in terms of elliptic functions and modular forms.
60 citations
Abstract: The elliptic genus Z_{BH} of a large class of 4D black holes can be expressed as an M-theory partition function on an AdS_3xS^2xCY_3 attractor. We approximate this partition function by summing over multiparticle chiral primary states of membranes which wrap curves in the CY_3 and tile Landau levels on the horizon S^2. Significantly, membranes and antimembranes can preserve the same supercharges if they occupy antipodal points on the horizon. It is shown the membrane contribution to Z_{BH} gives precisely the topological string partition function Z_{top} while the antimembranes give \bar Z_{top}, implying Z_{BH}=|Z_{top}|^2 in this approximation.
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TL;DR: In this article, the topological string partition function Z =exp(lambda 2g-2} F_g is calculated on a compact Calabi-Yau M. This defines it everywhere in the moduli space of M along with preferred local coordinates.
Abstract: The topological string partition function Z=exp(lambda^{2g-2} F_g) is calculated on a compact Calabi-Yau M. The F_g fulfill the holomorphic anomaly equations, which imply that Z transforms as a wave function on the symplectic space H^3(M,Z). This defines it everywhere in the moduli space of M along with preferred local coordinates. Modular properties of the sections F_g as well as local constraints from the 4d effective action allow us to fix Z to a large extend. Currently with a newly found gap condition at the conifold, regularity at the orbifold and the most naive bounds from Castelnuovos theory, we can provide the boundary data, which specify Z, e.g. up to genus 51 for the quintic.
TL;DR: It is found that the partition function zeros of the periodic and quasiperiodic quantum Ising chain lie on the circle at zero temperature and the radius equal to the values of the critical field.
Abstract: The partition function zeros of the anisotropic $XY$ chain in a complex transverse field are studied analytically and numerically. It is found that the partition function zeros of the periodic and quasiperiodic quantum Ising chain lie on the circle at zero temperature and the radius equal to the values of the critical field. For the periodic and quasiperiodic anisotropic $XY$ chains, the closed curves are split to two or three closed curves as the anisotropic parameter $\ensuremath{\gamma}$ decreases at a given ratio of two kinds of exchange interactions. For the isotropic $XX$ case, the partition function zeros lie on the straight segments which are parallel to the real axis and the segments move towards the real axis as the temperature goes to zero.
TL;DR: In this paper, the partition function for the topological Landau-Ginzburg B-model on the disk was derived by treating the worldsheet superpotential perturbatively.
Abstract: We compute the partition function for the topological Landau-Ginzburg B-model on the disk. This is done by treating the worldsheet superpotential perturbatively. We argue that this partition function as a function of bulk and boundary perturbations may be identified with the effective D-brane superpotential in the target spacetime. We point out the relationship of this approach to matrix factorizations. Using these methods, we prove a conjecture for the effective superpotential of Herbst, Lazaroiu and Lerche for the A-type minimal models. We also consider the Landau-Ginzburg theory of the cubic torus where we show that the effective superpotential, given by the partition function, is consistent with the one obtained by summing up disk instantons in the mirror A-model. This is done by explicitly constructing the open-string mirror map.
01 Jun 2006
TL;DR: In this paper, an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials was performed, where the authors improved and extended the earlier results by Brak, Essam and Owczarek.
Abstract: We perform an exact and asymptotic analysis of the model of n vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon configurations which start on the wall, but may end at arbitrary height, and their mean number of contacts with the wall. We improve and extend the earlier (partially nonrigorous) results by Brak, Essam and Owczarek, providing new exact results, and more precise and more general asymptotic results, in particular full asymptotic expansions for the partition function and the mean number of contacts. Furthermore, we relate this circle of problems to earlier results in the combinatorial and statistical literature.
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TL;DR: In this article, a hierarchy of differential equations which uniquely determine the coefficients in the asymptotic expansion, for large $N$, of the logarithm of the partition function of $N \times N$ Hermitian random matrices, is derived.
Abstract: In this paper we derive a hierarchy of differential equations which uniquely determine the coefficients in the asymptotic expansion, for large $N$, of the logarithm of the partition function of $N \times N$ Hermitian random matrices. These coefficients are generating functions for graphical enumeration on Riemann surfaces. The case that we particularly consider is for an underlying measure that differs from the Gaussian weight by a single monomial term of degree $2
u$. The coupling parameter for this term plays the role of the independent dynamical variable in the differential equations. From these equations one may deduce functional analytic characterizations of the coefficients in the asymptotic expansion. Moreover, this ode system can be solved recursively to explicitly construct these coefficients as functions of the coupling parameter. This analysis of the fine structure of the asymptotic coefficients can be extended to multiple coupling parameters and we present a limited illustration of this for the case of two parameters.
TL;DR: In this paper, two types of oscillator processes can be obtained as solutions to fractional Langevin equation based on Riemann-Liouville and Weyl fractional integro-differential operators.
01 Jan 2006
01 Jan 2006
TL;DR: This paper shows how to reconstruct multi-scale implicit surfaces with attributes, given those discrete point sets with attribute, and evaluates the advantages and drawbacks of the reconstruction method compared to existing reconstruction methods for implicit surfaces.
Abstract: Real-world 3D models are primarily acquired as large unorganized discrete point sets with attributes. In this paper, we show how to reconstruct multi-scale implicit surfaces with attributes, given those discrete point sets with attributes. In a preprocess, we first subdivide the global domain into overlapping local subdomains by computing a perfectly balanced binary tree. Second, we compute subsets of the points for the inner nodes of the tree for the intermediate resolutions bottom-up by using data thinning algorithms. Third, we reconstruct the surface parts in all nodes of the binary tree from the non-disjunct subsets of the points by using variational techniques with radial basis functions. For the evaluation of the defining function of the implicit surface at the desired scale, we hierarchically blend together the surface parts of the inner nodes by using a family of functions called partition of unity. Our new reconstruction method is particularly robust since the number of data points in the partition of unity blending zones can be specified explicitly. We show how our reconstruction method can also be applied to reconstruct continuous functions for the surface's attributes. In a short discussion, we evaluate the advantages and drawbacks of our reconstruction method compared to existing reconstruction methods for implicit surfaces.
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TL;DR: In this article, an expression of a deformed partition function for N = 2 U(1) gauge theory on C^2/Z_k by using plethystic exponentials is presented.
Abstract: We present an expression of a deformed partition function for N=2 U(1) gauge theory on C^2/Z_k by using plethystic exponentials.
TL;DR: In this article, the exact expression for the finite temperature two-point correlation function for the magnetization was rewritten as a partition function of some field theory, which removed singularities and provided a convenient form to develop a virial expansion (the expansion in powers of soliton density).
Abstract: We rewrite the exact expression for the finite temperature two-point correlation function for the magnetization as a partition function of some field theory. This removes singularities and provides a convenient form to develop a virial expansion (the expansion in powers of soliton density).
01 Jan 2006
TL;DR: In this article, it was shown that the phase transition between a phonon phase and a saddle phase corresponds to the dynamical phase transition in glasses, that has been studied in the framework of the mode coupling approximation.
Abstract: In this paper I will describe some results that have been recently obtained in the study of random Euclidean matrices, i.e. matrices that are functions of random points in Euclidean space. In the case of {\sl translation invariant} matrices one generically finds a phase transition between a {\sl phonon} phase and a {\sl saddle} phase. If we apply these considerations to the study of the Hessian of the Hamiltonian of the particles of a fluid, we find that this phonon-saddle transition corresponds to the dynamical phase transition in glasses, that has been studied in the framework of the mode coupling approximation. The Boson peak observed in glasses at low temperature is a remanent of this transition. We finally present some recent results obtained with a new approach where one deeply uses some hidden supersymmetric properties of the problem.
TL;DR: In this article, higher-order phase transitions characterized by both discontinuities and divergences are analyzed through the medium of partition function zeros, and properties of the distributions of zeros are derived, certain scaling relations are recovered and new ones are presented.
TL;DR: In this article, a model of directed polymers in a random environment with a positive recurrent Markov chain, taking values in a countable space Σ, was studied and the asymptotic behavior of the normalized partition function was characterized.
Abstract: We study a model of directed polymers in a random environment with a positive recurrent Markov chain, taking values in a countable space Σ. The random environment is a family (
$$g(i,x), i \geq 1,x \in \Sigma$$
) of independent and identically distributed real-valued variables. The asymptotic behaviour of the normalized partition function is characterized: when the common law of the g(·,·) is infinitely divisible and the Markov chain is exponentially recurrent we prove that the normalized partition function converges exponentially fast towards zero at all temperatures.
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TL;DR: In this article, a new solution to partition function form games is proposed, which is novel in at least two ways: first, the response to a deviation is established as the same solution applied to the residual game and second, a pair of solutions as the extrema of an interval for set inclusion.
Abstract: We present a new solution to partition function form games that is novel in at least two ways. Firstly, the solution exploits the consistency of the partition function form, namely that the response to a deviation is established as the same solution applied to the residual game, itself a partition function form game. This consistency allows us to model residual behaviour in a natural, intuitive way. Secondly, we consider a pair of solutions as the extrema of an interval for set inclusion. Taking the whole interval rather than just one of the extremes enables us to include or exclude outcomes with certainty.
TL;DR: The Erice Summer School 2005 Computer Simulations in Condensed Matter: from Materials to Chemical Biology as discussed by the authors was organized by Kurt Binder, Giovanni Ciccotti and Mauro Ferrario.
Abstract: Lecture Notes for the Erice Summer School 2005 Computer Simulations in Condensed Matter: from Materials to Chemical Biology. Perspectives in celebration of the 65th Birthday of Mike Klein organized by Kurt Binder, Giovanni Ciccotti and Mauro Ferrario
TL;DR: Kholodenko as discussed by the authors showed that Veneziano amplitude is the Laplace transform of the generating function for the Ehrhart polynomial for the regular inflated simplex obtained as deformation retract of the Fermat (hyper) surface living in the complex projective space.
TL;DR: In this article, the authors considered the partition function Z N of a random matrix model with polynomial potential V(ξ) = t 1 ξ + t 2 ξ 2 + ··· + T 2d ξ2d 2d, and derived the second logarithmic derivative of Z N with respect to the times t k can be expressed in terms of the recurrence coefficients of the related orthogonal polynomials.
Abstract: We consider the partition function Z N of a random matrix model with polynomial potential V(ξ) = t 1 ξ + t 2 ξ 2 + ··· + t 2d ξ 2d . It is known that the second logarithmic derivative of Z N with respect to the times t k can be expressed in terms of the recurrence coefficients of the related orthogonal polynomials. An explicit formula for the recurrence coefficients of the orthogonal polynomials in the limit N → oo for multi-cut regular V (ξ) has been derived in [ 10] through the Riemann-Hilbert approach. The expression for Z N in the limit N → ∞ has been derived in [7] through a mean-field approach. We show that the above asymptotic formulae satisfy the same relations that hold for finite N.
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TL;DR: In this article, it was shown that the skew-orthogonal polynomials associated to the partition function of the Gaussian Orthogonal Ensemble of random matrices with a potential function of degree n can be characterized by a Riemann-Hilbert problem.
Abstract: We find a local $(d+1) \times (d+1)$ Riemann-Hilbert problem characterizing the skew-orthogonal polynomials associated to the partition function of the Gaussian Orthogonal Ensemble of random matrices with a potential function of degree $d$. Our Riemann-Hilbert problem is similar to a local $d \times d$ Riemann-Hilbert problem found by Kuijlaars and McLaughlin characterizing the bi-orthogonal polynomials. This gives more motivation for finding methods to compute asymptotics of high order Riemann-Hilbert problems, and brings us closer to finding asymptotics of the skew-orthogonal polynomials.