28,848 research outputs found

### From N=2 Supergravity to Constrained Moduli Spaces

In this talk we review some results concerning a mechanism for reducing the
moduli space of a topological field theory to a proper submanifold of the
ordinary moduli space. Such mechanism is explicitly realized in the example of
constrained topological gravity, obtained by topologically twisting the N=2
Liouville theory.Comment: (Talk given at the Trieste Workshop on String Theory, April 1994)
LaTeX file, 17 pages, SISSA 66/94/EP, IFUM 470/F

### Vector Multiplets and the Phases of N = 2 Theories in 2D Through the Looking Glass

We extend Witten's discussion of actions related to the Landau-Ginzburg
description of Calabi-Yau hypersurfaces in weighted projective spaces to cover
the mirror class of models that include twisted chiral matter multiplets and a
newly discovered 2D, N = 2 twisted vector multiplet. Certain integrability
obstructions are observed that constrain the most general constructions
containing both matter and twisted matter simultaneously. It is conjectured
that knot invariants will ultimately play a role in describing the most general
such model.Comment: 11 page

### Gauge Fields and D-branes

We prove that self-dual gauge fields in type I superstring theory are
equivalent to configurations of Dirichlet 5-branes, by showing that the
world-sheet theory of a Dirichlet 1-brane moving in a background of 5-branes
includes an ``ADHM sigma model.'' This provides an explicit construction of the
equivalent self-dual gauge field. We also discuss type II.Comment: harvmac, 9p

### Anticommutativity Equation in Topological Quantum Mechanics

We consider topological quantum mechanics as an example of topological field
theory and show that its special properties lead to numerous interesting
relations for topological corellators in this theory. We prove that the
generating function $\mathcal{F}$ for thus corellators satisfies the
anticommutativity equation $(\mathcal{D}- \mathcal{F})^2=0$. We show that the
commutativity equation $[dB,dB]=0$ could be considered as a special case of the
anticommutativity equation.Comment: 6 pages, no figures, Late

### Monopole Condensates in Seiberg-Witten Theory

A product of two Riemann surfaces of genuses p_1 and p_2 solves the
Seiberg-Witten monopole equations for a constant Weyl spinor that represents a
monopole condensate. Self-dual electromagnetic fields require p_1=p_2=p and
provide a solution of the euclidean Einstein-Maxwell-Dirac equations with p-1
magnetic vortices in one surface and the same number of electric vortices in
the other. The monopole condensate plays the role of cosmological constant. The
virtual dimension of the moduli space is zero, showing that for given p_1 and
p_2, the solutions are unique.Comment: 10 page

### Topological Massive Sigma Models

In this paper we construct topological sigma models which include a potential
and are related to twisted massive supersymmetric sigma models. Contrary to a
previous construction these models have no central charge and do not require
the manifold to admit a Killing vector. We use the topological massive sigma
model constructed here to simplify the calculation of the observables. Lastly
it is noted that this model can be viewed as interpolating between topological
massless sigma models and topological Landau-Ginzburg models.Comment: 20 pages, Phyzzx. Revised version to appear in Nucl. Phys. B. The
construction of the model is clarified and there are a few minor change

### The Mathai-Quillen Formalism and Topological Field Theory

These lecture notes give an introductory account of an approach to
cohomological field theory due to Atiyah and Jeffrey which is based on the
construction of Gaussian shaped Thom forms by Mathai and Quillen. Topics
covered are: an explanation of the Mathai-Quillen formalism for finite
dimensional vector bundles; the definition of regularized Euler numbers of
infinite dimensional vector bundles; interpretation of supersymmetric quantum
mechanics as the regularized Euler number of loop space; the Atiyah-Jeffrey
interpretation of Donaldson theory; the construction of topological gauge
theories from infinite dimensional vector bundles over spaces of connections.Comment: 34 a4.sty pages (Notes of lectures given at the Karpacz Winter School
on `Infinite Dimensional Geometry in Physics', 17-27 February 1992

### The d=6, (2,0)-tensor multiplet coupled to self-dual strings

We show that the central charges that group theory allows in the (2,0)
supersymmetry translations algebra arise from a string and a 3-brane by
commuting two supercharges. We show that the net force between two such
parallel strings vanishes. We show that all the coupling constants are fixed
numbers, due to supersymmetry, and self-duality of the three-form field
strength. We obtain a charge quantization for the self-dual field strength, and
show that when compactifying on a two-torus, it reduces to the usual
quantization condition of N=4 SYM with gauge group SU(2), and with coupling
constant and theta angle given by the tau-parameter of the two-torus, provided
that we pick that chiral theory which corresponds to a theta function with zero
characteristics, as expected on manifolds of this form.Comment: 18 pages, reference adde

### Global U(1) R-Symmetry And Conformal Invariance Of (0,2) Models

We derive a condition under which (0,2) linear sigma models possess a
``left-moving'' conformal stress tensor in \bq cohomology (i.e. which leaves
invariant the ``right-moving'' ground states) even away from their critical
points. At the classical level this enforces quasihomogeneity of the
superpotential terms. The persistence of this structure at the quantum level on
the worldsheet is obstructed by an anomaly unless the charges and
superpotential degrees satisfy a condition which is equivalent to the condition
for the cancellation of the anomaly in a particular ``right-moving'' U(1)
R-symmetry.Comment: 8 page

### On mixed phases in gauge theories

In many gauge theories at different values of parameters entering Lagrangian,
the vacuum is dominated by coherent condensates of different mutually non-local
fields (for instance, by condensates of electric or magnetic charges, or by
various dyons). It is argued that the transition between these "dual to each
other" phases proceeds through the intermediate "mixed phase", having
qualitatively different features. The examples considered include: ordinary YM,
N=1 SYM, N=1 SQCD, and broken N=2 SYM and SQCD.Comment: Latex, 19 pages; Talk given at "Continuous Advances in
QCD-2002/Arkadyfest", honoring the 60-th birthday of Arkady Vainshtein; 17-23
May 2002, University of Minneapolis, Minnesota, USA; v.3: the extended and
improved versio

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