Paul Windey

Quantum mechanics and the geometry of the Weyl character formula

Abstract General field theoretic methods are developed which will allow a path integral derivation of the character formula for loop groups. The methods are introduced in the classical Weyl character case. The irreducible representations of a compact semi-simple Lie group G are realized as the ground states of a supersymmetric quantum mechanical system. The Hilbert space for the quantum mechanical system is the space of sections of a holomorphic line bundle L over the complex manifold G/T, where T is the maximal torus of G. The Weyl character formula is derived by an explicit path integral computation of the index of the Dolbeault operator ∂ L .

The Black hole entropy can be smaller than A/4

Abstract The coupling of a Nambu-Goto string to gravity allows for Schwarzschild black holes whose entropy to area relation is S = ( A 4 )(1 − 4μ) , where μ is the string tension.

Universality in two-dimensional quantum gravity

Abstract We present a new definition of the continuum limit in the random triangulation formulation of two-dimensional quantum gravity. This method uses a diffusion equation describing random walks in the space of orthogonal polynomials as the defining equation of the theory. This leads to a simple proof for universality of any potential and a direct connection of the KdV hierarchy.

Progress in string theory and M-theory

Preface. Lectures. Scales of String/M Theory C. Bachas. On the Heterotic/F-Theory Duality in Eight Dimensions W. Lerche. Large N Field Theories, String Theory and Gravity J. Maldacena. Black Holes and the Phases of Brane Thermodynamics E.J. Martinec. Non-BPS-D-Brane Systems J.H. Schwarz. Non-BPS States and Branes in String Theory A. Sen. Lectures on Superconformal Quantum Mechanics and Multi-Black Hole Moduli Spaces A. Strominger. Brane Theory Solitons P.K. Townsend. Gong Show. D-Branestrahlung M. Abou-Zaid, M.S. Costa. Strings on BTZ Black Holes R. Argurio. A Note on non-supersymmetric Open-String Orbifolds with a quantised Bab C. Angelantonj. On the Non-Abelian Born-Infeld Action P. Bain. AdS3 asymptotic (super)Symmetries K. Bautier. Anomalous couplings of Non-BPS D-Branes M. Billo, et al. From a Conformal Anomaly to a Theory of Tensionless Strings? R.A. Corrado. Comments on non-supersymmetric type I vacua K. Forger. S-Matrices for Planckian Scattering S. de Haro. K-Theory and D-Branes on NON-Commutative Tori S. Gukov. Generalized Calibrations J. Gutowski. Aspects of Heterotic/M-Theory Duality in D=3 M. Haack, J. Louis. Gauge Theory scattering from the ADS/CFT correspondence R.A. Janik. Flat Connections for Yang-Mills Theories on the 3-Torus A. Keurentjes. From Topological Field Theories to Covariant Matrix Strings L. Baulieu, et al. Field Theory Duals from (Non)-Crital Type 0 Strings D. Martelli. Duality and Selfduality of Chiral Boson Fields in various Dimensions A. Maznytsia, et al. Anti-de Sitter Fragmentation J. Michelson. On ADS3 String Theory P.M. Petropoulos.Spectrum of D= 11 Supergravity on ADS2 x S2 x T7 S. Lee. Discrete U-duality groups G. Schroder. Supersymmetric Worldvolume Solitons J. Simon. WZ Couplings of D-Branes and O-Planes B. Stefanski, jr. Holography for Coset Spaces A. Volovich. Appendix. List of Speakers. List of Participants.

The supersymmetric σ-model and the geometry of the Weyl-Kač character formula

Abstract Field theoretic and geometric ideas are used to construct a chiral supersymmetric field theory for which the ground state is a specified irreducible representation of a centrally extended loop group. The character index of the associated supercharge (an appropriate Dirac operator on LG/T) is the Weyl-Kac character formula which we compute explicitly by the steepest-descent approximation.

Black hole entropy and string instantons

Abstract The coupling of a string to gravity allows for Schwarzschild black holes whose entropy to area relation is S = 1 4 A( 1 /-t4μ) , where μ is the string tension. This departure from the 1 4 A universality results from a string instanton generating a black hole with smaller entropy at a temperature exceeding the Hawking value. The temperature is sensitive to the presence of classical matter outside the black hole horizon but the entropy is not. The horizon materializes at the quantum level. It is conjectured that such a macroscopic non-local effect may be operative in retrieving information from incipient black holes.

Quantum Field Theory and String Theory

Fractal Structure in 4d Gravity -- A One Dimensional Ideal Gas of Spinons, or Some Exact Results on the XXX Spin Chain with Long Range Interaction -- Kodaira-Spencer Theory of Gravity -- 3d Gravity and Gauge Theories -- On the W-Gravity Spectrum and its G-Structure -- Light-Cone Quantization of Matrix Models at c>1 -- Multicritical Points of 2-Matrix Models -- The Super Self-Dual Matreoshka -- The Phenomenology of Strings and Clusters in the 3-d Ising Model -- Conformai Field Theory Techniques in Large N Yang-Mills Theory -- to Differential W-Geometry -- Topological Strings and QCD in Two Dimensions -- Continuum QCD2 in Terms of Discrete Random Surfaces with Local Weights -- Strings and Causality -- Loop Equation and Area Law in Turbulence -- The Two-Dimensional String as a Topological Field Theory -- Linear Systems for 2d Poincare Supergravities -- Quantization of Mirror Symmetry -- Integrable Qft2 Encoded on Products of Dynkin Diagrams -- Remarks on Topological String Theories -- Hamiltonian Reduction of the BRST Complex and N=2 SUSY -- Lattice Models and N=2 Supersymmetry -- Canonical Construction of Liouville Field Operators with Arbitrary Spin -- Bethe Ansatz for the Bloch Particle in Magnetic Field.

Analytic index for a family of Dirac-Ramond operators.

We derive a cohomological formula for the analytic index of a family of Dirac–Ramond operators and exhibit its modular properties.

Progress in string, field and particle theory

Preface. I: Lectures. The non-ADS / non-CFT correspondence, or three different paths to QCD O. Aharony. Physics of low scale string models I. Antoniadis. Supergravityversus topological gravity L. Baulieu. The holographic principle R. Bousso. Two talks on a tentative theory of large distance physics D. Friedan. A toy model for the M5-brane J. Harvey. D-branes on the conifiold and Nu = 1 gauge/gravity dualities C.P. Herzog, et al. Defects, decay, and dissipated states E.J. Martinec. String dynamics on PP-waves from Yang Mills theory S. Minwalla. Seiberg Witten prepotential, higher Casimirs, and free fermions N.A. Nekrasov. Aspects of string motion in time-dependent backgrounds E. Rabinovici. On the geometry of higher-spin gauge fields D. Francia, A. Sagnotti. Open string creation by S-branes A. Strominger. Topics in gauge theory/string theory duality E. Verlinde. Open string star algebra and rolling tachyons B. Zwiebach. II: Gong Show. Appendix. List of speakers. List of participants.

Diffusion Equation, Continuum Limit and Universality in Two Dimensional Quantum Gravity

In this paper we will present a brief summary of the definition of the continuum limit of the matrix model description of two dimensional gravity using a diffusion equation. This method differs from the continuum limit originally presented in [1, 2, 7] in the following way: the continuum limit in these papers is obtained by firstly computing the matrix elements of a certain operator and subsequently taking the continuum limit of the matrix elements. In this article we use a different approach. We derive an exact difference equation satisfied by the matrix elements and subsequently take the continuum limit of this equation. The continuum differential equation is then used to define the continuum limit of the original matrix elements in a totally consistent way. Both these methods lead to the same universal behavior as seen by explicit examples.