Philippe Pouliot

The University of Texas at Austin

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Amir Kashani-Poor

École Normale Supérieure

R. P. Langlands

Institute for Advanced Study

Sònia Paban

The University of Texas at Austin

Elie Gorbatov

University of California, San Diego

Willy Fischler

The University of Texas at Austin

Yvan Saint-Aubin

Université de Montréal

Matthew J. Strassler

Harvard University

Daniel Kabat

City University of New York

Michael R. Douglas

Stony Brook University

Joaquim Gomis

Institut de Ciències del Cosmos

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Institute for Advanced Study

Rutgers, The State University of New Jersey

The University of Texas at Austin

Harvard University

University of California, Santa Barbara

Stanford University

Princeton University

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Massachusetts Institute of Technology

Stony Brook University

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Finite number of states, de Sitter space and quantum groups at roots of unity

Classical and Quantum Gravity (2003)

Philippe Pouliot

This paper explores the use of a deformation by a root of unity as a tool to build models with a finite number of states for applications to quantum gravity. The initial motivation for this work was cosmological breaking of supersymmetry. We explain why the project was unsuccessful. What is left are some observations on supersymmetry for q-bosons, an analogy between black holes in de Sitter and properties of quantum groups, and an observation on a noncommutative quantum mechanics model with two degrees of freedom, depending on one parameter. When this parameter is positive, the spectrum has a finite number of states; when it is negative or zero, the spectrum has an infinite number of states. This exhibits a desirable feature of quantum physics in de Sitter space, albeit in a very simple, non-gravitational context.

10.1088/0264-9381/21/1/010

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A chiral SU(N) gauge theory and its non-chiral Spin(8) dual

Physics Letters B (1996)

Philippe Pouliot Matthew J. Strassler

10.1016/0370-2693(95)01554-x

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Citations (53)

Molien function for duality

Journal of High Energy Physics (1999)

Philippe Pouliot

Duality (order theory)

Seiberg duality

Representation

Superfield

10.1088/1126-6708/1999/01/021

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Citations (41)

Duality and dynamical supersymmetry breaking in Spin(10) with a spinor

Physics Letters B (1996)

Philippe Pouliot Matthew J. Strassler

Duality (order theory)

Seiberg duality

10.1016/0370-2693(96)00241-9

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Citations (41)

Conformal invariance in two-dimensional percolation

arXiv (Cornell University) (1994)

R. P. Langlands Philippe Pouliot Yvan Saint-Aubin

The immediate purpose of the paper was neither to review the basic definitions of percolation theory nor to rehearse the general physical notions of universality and renormalization (an important technique to be described in Part Two). It was rather to describe as concretely as possible, although in hypothetical form, the geometric aspects of universality, especially conformal invariance, in the context of percolation, and to present the numerical results that support the hypotheses. On the other hand, one ulterior purpose is to draw the attention of mathematicians to the mathematical problems posed by the physical notions. Some precise basic definitions are necessary simply to orient the reader. Moreover a brief description of scaling and universality on the one hand and of renormalization on the other is also essential in order to establish their physical importance and to clarify their mathematical content.

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Quantum determinism for free vector bosons in 3 dimensions

Journal of High Energy Physics (2001)

Philippe Pouliot

Vector boson

10.1088/1126-6708/2001/11/028

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Citations (2)

(S)quark masses and non-Abelian horizontal symmetries

Physics Letters B (1993)

Philippe Pouliot Nathan Seiberg

10.1016/0370-2693(93)91801-s

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Citations (93)

Conformal invariance in two-dimensional percolation

Bulletin of the American Mathematical Society (1994)

R. P. Langlands Philippe Pouliot Yvan Saint-Aubin

The word percolation, borrowed from the Latin, refers to the seeping or oozing of a liquid through a porous medium, usually to be strained. In this and related senses it has been in use since the seventeenth century. It was introduced more recently into mathematics by S. R. Broadbent and J. M. Hammersley ([BH]) and is a branch of probability theory that is especially close to statistical mechanics. Broadbent and Hammersley distinguish between two types of spreading of a fluid through a medium, or between two aspects of the probabilistic models of such processes: diffusion processes, in which the random mechanism is ascribed to the fluid; and percolation processes, in which it is ascribed to the medium. A percolation process typically depends on one or more probabilistic parameters. For example, if molecules of a gas are absorbed at the surface of a porous solid (as in a gas mask) then their ability to penetrate the solid depends on the sizes of the pores in it and their positions, both conceived to be distributed in some random manner. A simple mathematical model of such a process is often defined by taking the pores to be distributed in some regular manner (that could be determined by a periodic graph), and to be open (thus very large) or closed (thus smaller than the molecules) with probabilities p and 1 − p. As p increases the probability of deeper penetration of the gas into the interior of the solid grows.

Percolation (cognitive psychology)

10.1090/s0273-0979-1994-00456-2

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Citations (204)

Spectroscopy of gauge theories based on exceptional Lie groups

Journal of Physics A Mathematical and General (2001)

Philippe Pouliot

We generate by computer a basis of invariants for the fundamental representations of the exceptional Lie groups E6 and E7, up to degree 18. We discuss the relevance of this calculation for the study of supersymmetric gauge theories, and revisit the self-dual exceptional models. We study the chiral ring of G2 to degree 13, as well as a few classical groups. The homological dimension of a ring is a natural estimator of its complexity and provides a guideline for identifying theories that have a good chance to be amenable to a solution.

Simple Lie group

Degree (music)

10.1088/0305-4470/34/41/317

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Citations (11)

The interplay between θ and T

Journal of High Energy Physics (2000)

Willy Fischler Elie Gorbatov Amir Kashani-Poor Robert McNees Sònia Paban

Statistical Mechanics

Thermal fluctuations

10.1088/1126-6708/2000/06/032

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Citations (25)