1,137 research outputs found
Nonrenormalization Theorem for Gauge Coupling in 2+1D
We prove that \be-function of the gauge coupling in gauge theory
coupled to any renormalizable system of spinor and scalar fields is zero. This
result holds both when the gauge field action is the Chern-Simons action and
when it is the topologically massive action.Comment: 8 pages, LaTeX file, CALT-68-191
Tests of Seiberg-like Duality in Three Dimensions
We use localization techniques to study several duality proposals for
supersymmetric gauge theories in three dimensions reminiscent of Seiberg
duality. We compare the partition functions of dual theories deformed by real
mass terms and FI parameters. We find that Seiberg-like duality for N=3
Chern-Simons gauge theories proposed by Giveon and Kutasov holds on the level
of partition functions and is closely related to level-rank duality in pure
Chern-Simons theory. We also clarify the relationship between the
Giveon-Kutasov duality and a duality in theories of fractional M2 branes and
propose a generalization of the latter. Our analysis also confirms previously
known results concerning decoupled free sectors in N=4 gauge theories realized
by monopole operators.Comment: 36 pages, 5 figure
On S-duality for Non-Simply-Laced Gauge Groups
We point out that for N=4 gauge theories with exceptional gauge groups G_2
and F_4 the S-duality transformation acts on the moduli space by a nontrivial
involution. We note that the duality groups of these theories are the Hecke
groups with elliptic elements of order six and four, respectively. These groups
extend certain subgroups of SL(2,Z) by elements with a non-trivial action on
the moduli space. We show that under an embedding of these gauge theories into
string theory, the Hecke duality groups are represented by T-duality
transformations.Comment: 8 pages, latex. v2: references adde
Isotropic A-branes and the stability condition
The existence of a new kind of branes for the open topological A-model is
argued by using the generalized complex geometry of Hitchin and the SYZ picture
of mirror symmetry. Mirror symmetry suggests to consider a bi-vector in the
normal direction of the brane and a new definition of generalized complex
submanifold. Using this definition, it is shown that there exists generalized
complex submanifolds which are isotropic in a symplectic manifold. For certain
target space manifolds this leads to isotropic A-branes, which should be
considered in addition to Lagrangian and coisotropic A-branes. The Fukaya
category should be enlarged with such branes, which might have interesting
consequences for the homological mirror symmetry of Kontsevich. The stability
condition for isotropic A-branes is studied using the worldsheet approach.Comment: 19 page
AGT on the S-duality Wall
Three-dimensional gauge theory T[G] arises on a domain wall between
four-dimensional N=4 SYM theories with the gauge groups G and its S-dual G^L.
We argue that the N=2^* mass deformation of the bulk theory induces a
mass-deformation of the theory T[G] on the wall. The partition functions of the
theory T[SU(2)] and its mass-deformation on the three-sphere are shown to
coincide with the transformation coefficient of Liouville one-point conformal
block on torus under the S-duality.Comment: 14 pages, 3 figures. v2: Revised the analysis in sections 3.3 and 4.
Notes and references added. Version to appear in JHE
Topological strings on noncommutative manifolds
We identify a deformation of the N=2 supersymmetric sigma model on a
Calabi-Yau manifold X which has the same effect on B-branes as a noncommutative
deformation of X. We show that for hyperkahler X such deformations allow one to
interpolate continuously between the A-model and the B-model. For generic
values of the noncommutativity and the B-field, properties of the topologically
twisted sigma-models can be described in terms of generalized complex
structures introduced by N. Hitchin. For example, we show that the path
integral for the deformed sigma-model is localized on generalized holomorphic
maps, whereas for the A-model and the B-model it is localized on holomorphic
and constant maps, respectively. The geometry of topological D-branes is also
best described using generalized complex structures. We also derive a
constraint on the Chern character of topological D-branes, which includes
A-branes and B-branes as special cases.Comment: 36 pages, AMS latex. v2: a reference to a related work has been
added. v3: An error in the discussion of the Fourier-Mukai transform for
twisted coherent sheaves has been fixed, resulting in several changes in
Section 2. The rest of the paper is unaffected. v4: an incorrect statement
concerning Lie algebroid cohomology has been fixe
- …