1,667 research outputs found
Topological Chern-Simons Sigma Model
We consider topological twisting of recently constructed Chern-Simons-matter
theories in three dimensions with N=4 or higher supersymmetry. We enumerate
physically inequivalent twistings for each N, and find two different twistings
for N=4, one for N=5,6, and four for N=8. We construct the two types of N=4
topological theories, which we call A/B-models, in full detail. The A-model has
been recently studied by Kapustin and Saulina. The B-model is new and it
consists solely of a Chern-Simons term of a complex gauge field up to
BRST-exact terms. We also compare the new theories with topological Yang-Mills
theories and find some interesting connections. In particular, the A-model
seems to offer a new perspective on Casson invariant and its relation to
Rozansky-Witten theory.Comment: 31 pages, no figure; v2. references adde
Covariant Quantization of the Brink-Schwarz Superparticle
The quantization of the Brink-Schwarz-Casalbuoni superparticle is performed
in an explicitly covariant way using the antibracket formalism. Since an
infinite number of ghost fields are required, within a suitable off-shell
twistor-like formalism, we are able to fix the gauge of each ghost sector
without modifying the physical content of the theory. The computation reveals
that the antibracket cohomology contains only the physical degrees of freedom.Comment: 24 page
Electric-Magnetic Duality And The Geometric Langlands Program
The geometric Langlands program can be described in a natural way by
compactifying on a Riemann surface C a twisted version of N=4 super Yang-Mills
theory in four dimensions. The key ingredients are electric-magnetic duality of
gauge theory, mirror symmetry of sigma-models, branes, Wilson and 't Hooft
operators, and topological field theory. Seemingly esoteric notions of the
geometric Langlands program, such as Hecke eigensheaves and D-modules, arise
naturally from the physics.Comment: 225 pp; further clarification
Dynkin Diagrams and Integrable Models Based on Lie Superalgebras
An analysis is given of the structure of a general two-dimensional Toda field
theory involving bosons and fermions which is defined in terms of a set of
simple roots for a Lie superalgebra. It is shown that a simple root system for
a superalgebra has two natural bosonic root systems associated with it which
can be found very simply using Dynkin diagrams; the construction is closely
related to the question of how to recover the signs of the entries of a Cartan
matrix for a superalgebra from its Dynkin diagram. The significance for Toda
theories is that the bosonic root systems correspond to the purely bosonic
sector of the integrable model, knowledge of which can determine the bosonic
part of the extended conformal symmetry in the theory, or its classical mass
spectrum, as appropriate. These results are applied to some special kinds of
models and their implications are investigated for features such as
supersymmetry, positive kinetic energy and generalized reality conditions for
the Toda fields. As a result, some new families of integrable theories with
positive kinetic energy are constructed, some containing a mixture of massless
and massive degrees of freedom, others being purely massive and supersymmetric,
involving a number of coupled sine/sinh-Gordon theories.Comment: 31 pages; plain TeX, macros included; 5 main Figs., more in tables;
v2: minor but confusing inaccuracy corrected in statement of one proposition
(already corrected in published version
Membrane Quantum Mechanics
We consider the multiple M2-branes wrapped on a compact Riemann surface and
study the arising quantum mechanics by taking the limit where the size of the
Riemann surface goes to zero. The IR quantum mechanical models resulting from
the BLG-model and the ABJM-model compactified on a torus are N = 16 and N = 12
superconformal gauged quantum mechanics. After integrating out the auxiliary
gauge fields we find OSp(16|2) and SU(1,1|6) quantum mechanics from the reduced
systems. The curved Riemann surface is taken as a holomorphic curve in a
Calabi-Yau space to preserve supersymmetry and we present a prescription of the
topological twisting. We find the N = 8 superconformal gauged quantum mechanics
that may describe the motion of two wrapped M2-branes in a K3 surface.Comment: 54 pages, v2: errors corrected and notations improve
Lectures on Mirror Symmetry, Derived Categories, and D-branes
This paper is an introduction to Homological Mirror Symmetry, derived
categories, and topological D-branes aimed mainly at a mathematical audience.
In the paper we explain the physicists' viewpoint of the Mirror Phenomenon, its
relation to derived categories, and the reason why it is necessary to enlarge
the Fukaya category with coisotropic A-branes; we discuss how to extend the
definition of Floer homology to such objects and describe mirror symmetry for
flat tori. The paper consists of four lectures which were given at the
Institute for Pure and Applied Mathematics (Los Angeles), March 2003, as part
of a program on Symplectic Geometry and Physics.Comment: 30 page
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