802 publications from this institution
It is shown that 2+1 dimensional quantum Yang-Mills theory, with an action consisting purely of the Chern-Simons term, is exactly soluble and gives a natur
A bstract It has been proposed that a certain ℤ N orbifold, analytically continued in N , can be used to describe the thermodynamics of Rindler space in string theory. In this paper, we attempt to implement this idea for the open-string sector. The most interesting result is that, although the orbifold is tachyonic for positive integer N , the tachyon seems to disappear after analytic continuation to the region that is appropriate for computing Tr $$ {\rho}^{\mathcal{N}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>ρ</mml:mi> <mml:mi>N</mml:mi> </mml:msup> </mml:math> , where ρ is the density matrix of Rindler space and Re $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> > 1. Analytic continuation of the full orbifold conformal field theory remains a challenge, but we find some evidence that if such analytic continuation is possible, the resulting theory is a logarithmic conformal field theory, necessarily nonunitary.
MOST expositions of string theory focus on its possible use as a framework for unifying the forces of nature. But I will take a different tack in this article. Rather than the unification of the forces, I will here describe what one might call the unification of the ideas.
We study a 3-dimensional topological sigma-model, whose target space is a hyper-Kahler manifold X. A Feynman diagram calculation of its partition function demonstrates that it is a finite type invariant of 3-manifolds which is similar in structure to those appearing in the perturbative calculation of the Chern-Simons partition function. The sigma-model suggests a new system of weights for finite type invariants of 3-manifolds, described by trivalent graphs. The Riemann curvature of X plays the role of Lie algebra structure constants in Chern-Simons theory, and the Bianchi identity plays the role of the Jacobi identity in guaranteeing the so-called IHX relation among the weights. We argue that, for special choices of X, the partition function of the sigma-model yields the Casson-Walker invariant and its generalizations. We also derive Walker's surgery formula from the SL(2,Z) action on the finite-dimensional Hilbert space obtained by quantizing the sigma-model on a two-dimensional torus.
This paper is devoted in part to clarifying some aspects of the relation between quantum field theory and infinite Grassmannians, and in part to pointing o
These are notes on the theory of supermanifolds and integration on them, aiming to collect results that are useful for a better understanding of superstring perturbation theory in the RNS formalism.
We discuss some general properties of quantum gravity in De Sitter space. It has been argued that the Hilbert space is of finite dimension. This suggests a macroscopic argument that General Relativity cannot be quantized -- unless it is embedded in a more precise theory that determines the value of the cosmological constant. We give a definition of the quantum Hilbert space using the asymptotic behavior in the past and future, without requiring detailed microscopic knowledge. We discuss the difficulties in defining any precisely calculable or measurable observables in an asymptotically de Sitter spacetime, and explore some meta-observables that appear to make mathematical sense but cannot be measured by an observer who lives in the spacetime. This article is an expanded version of a lecture at Strings 2001 in Mumbai.
We study a 3-dimensional topological sigma-model, whose target space is a hyper-Kähler manifold X. A Feynman diagram calculation of its partition func
We investigate the statistical mechanics of a gas of fractional statistics particles in 2 + 1 dimensions. In the case of statistics very close to Fermi statistics (statistical parameter θ = π(1 − 1/n), for large n), the effect of the statistics is a weak attraction. Building upon earlier RPA calculation of Fetter, Hanna, and Laughlin for the case n = 2, we argue that for large n perturbation theory is reliable and exhibits superfluidity (or superconductivity after coupling to electromagnetism). We attempt to describe the order parameter of this superconducting phase in terms of "spontaneous breaking of commutativity of translations" as opposed to the usual pairing order parameters. The vortices of the superconducting anyon gas are charged, and superconducting order parameters of the usual type vanish. We investigate the characteristic P and T violating phenomenology.
These are notes on the theory of super Riemann surfaces and their moduli spaces, aiming to collect results that are useful for a better understanding of superstring perturbation theory in the RNS formalism.
We generalize the recently discovered relationship between JT gravity and double-scaled random matrix theory to the case that the boundary theory may have time-reversal symmetry and may have fermions with or without supersymmetry. The matching between variants of JT gravity and matrix ensembles depends on the assumed symmetries. Time-reversal symmetry in the boundary theory means that unorientable spacetimes must be considered in the bulk. In such a case, the partition function of JT gravity is still related to the volume of the moduli space of conformal structures, but this volume has a quantum correction and has to be computed using Reidemeister-Ray-Singer torsion. Presence of fermions in the boundary theory (and thus a symmetry $(-1)^F$) means that the bulk has a spin or pin structure. Supersymmetry in the boundary means that the bulk theory is associated to JT supergravity and is related to the volume of the moduli space of super Riemann surfaces rather than of ordinary Riemann surfaces. In all cases we match JT gravity or supergravity with an appropriate random matrix ensemble. All ten standard random matrix ensembles make an appearance -- the three Dyson ensembles and the seven Altland-Zirnbauer ensembles. To facilitate the analysis, we extend to the other ensembles techniques that are most familiar in the case of the original Wigner-Dyson ensemble of hermitian matrices. We also generalize Mirzakhani's recursion for the volumes of ordinary moduli space to the case of super Riemann surfaces.
We present a new construction of the quantum Hubert space of Chern-Simons gauge theory using methods which are natural from the threedimensional point of view.To show that the quantum Hubert space associated to a Riemann surface Σ is independent of the choice of complex structure on Σ, we construct a natural projectively flat connection on the quantum Hubert bundle over Teichmuller space.This connection has been previously constructed in the context of two-dimensional conformal field theory where it is interpreted as the stress energy tensor.Our construction thus gives a (2 + 1 )-dimensional derivation of the basic properties of (1 + 1)-dimensional current algebra.To construct the connection we show generally that for affine symplectic quotients the natural projectively flat connection on the quantum Hubert bundle may be expressed purely in terms of the intrinsic Kahler geometry of the quotient and the Quillen connection on a certain determinant line bundle.The proof of most of the properties of the connection we construct follows surprisingly simply from the index theorem identities for the curvature of the Quillen connection.As an example, we treat the case when Σ has genus one explicitly.We also make some preliminary comments concerning the Hubert space structure.
A new mathematical framework for the Wess-Zumino chiral effective action is described. It is shown that this action obeys an a priori quantization law, analogous to Dirac's quantization of magnetic change. It incorporates in current algebra both perturbative and non-perturbative anomalies.
No abstract is provided for this article.
Making use of known facts about "tensor models," it is possible to construct a quantum system without quenched disorder that has the same large $n$ limit for its correlation functions and thermodynamics as the SYK model. This might be useful in further probes of this approach to holographic duality.
No abstract is provided for this article.
