713 research outputs found
On N=2 MQCD
We review M-theory description of 4d N=2 SQCD. Configurations of M-theory
fivebranes relevant to describe the moduli spaces of the Coulomb and Higgs
branches are studied using the Taub-NUT geometry. Minimal area membranes
related with the BPS states of N=2 SQCD are given explicitly. They almost
saturate the BPS bounds. The deviation from the bounds is due to their boundary
condition constrained by the fivebrane. The electric-magnetic duality at the
baryonic branch root is also examined from the M-theory viewpoint. In this
course, novel concepts such as creation of brane and exchange of branes in Type
II theory are explained in the framework of M-theory.Comment: 32 pages. 4 figires. Lecture in the Second Winter School on ``Branes,
Fields And Mathematical Physics" at the APCTP (Feb.9-20, 1998
Three-dimensional Black Holes and Liouville Field Theory
A quantization of (2+1)-dimensional gravity with negative cosmological
constant is presented and quantum aspects of the (2+1)-dimensional black holes
are studied thereby. The quantization consists of two procedures. One is
related with quantization of the asymptotic Virasoro symmetry. A notion of the
Virasoro deformation of 3-geometry is introduced. For a given black hole, the
deformation of the exterior of the outer horizon is identified with a product
of appropriate coadjoint orbits of the Virasoro groups .
Its quantization provides unitary irreducible representations of the Virasoro
algebra, in which state of the black hole becomes primary. To make the
quantization complete, holonomies, the global degrees of freedom, are taken
into account. By an identification of these topological operators with zero
modes of the Liouville field, the aforementioned unitary representations
reveal, as far as , as the Hilbert space of this two-dimensional
conformal field theory. This conformal field theory, living on the cylinder at
infinity of the black hole and having continuous spectrums, can recognize the
outer horizon only as a it one-dimensional object in and
realize it as insertions of the corresponding vertex operator. Therefore it can
not be a conformal field theory on the horizon. Two possible descriptions of
the horizon conformal field theory are proposed.Comment: 39 pages, LaTeX, 8 figures are added. Section 4.3 is revised and
enlarged to include the case of conical singularities. Several typos are
corrected. References are adde
Integrable Structure of Supersymmetric Yang-Mills and Melting Crystal
We study loop operators of SYM in background.
For the case of U(1) theory, the generating function of correlation functions
of the loop operators reproduces the partition function of melting crystal
model with external potential. We argue the common integrable structure of
SYM and melting crystal model.Comment: 12 pages, 1 figure, based on an invited talk presented at the
international workshop "Progress of String Theory and Quantum Field Theory"
(Osaka City University, December 7-10, 2007), to be published in the
proceeding
N=2 Supersymmetric Sigma Models and D-branes
We study D-branes of N=2 supersymmetric sigma models. Supersymmetric
nonlinear sigma models with 2-dimensional target space have D0,D1,D2-branes,
which are realized as A-,B-type supersymmetric boundary conditions on the
worldsheet. When we embed the models in the string theory, the Kahler potential
is restricted and leads to a 2-dim black hole metric with a dilaton background.
The D-branes in this model are susy cycles and consistent with the analysis of
conjugacy classes. The generalized metrics with U(n) isometry is proposed and
dynamics on them are realized by linear sigma models. We investigate D-branes
of the linear sigma models and compare the results with those in the nonlinear
sigma models.Comment: 23 pages, 5 figure
q -Difference Kac-Schwarz Operators in Topological String Theory
The perspective of Kac-Schwarz operators is introduced to the authors' previous work on the quantum mirror curves of topological string theory in strip geometry and closed topological vertex. Open string amplitudes on each leg of the web diagram of such geometry can be packed into a multi-variate generating function. This generating function turns out to be a tau function of the KP hierarchy. The tau function has a fermionic expression, from which one finds a vector |W⟩ in the fermionic Fock space that represents a point W of the Sato Grassmannian. |W⟩ is generated from the vacuum vector |0⟩ by an operator g on the Fock space. g determines an operator G on the space V=C((x)) of Laurent series in which W is realized as a linear subspace
Melting Crystal, Quantum Torus and Toda Hierarchy
Searching for the integrable structures of supersymmetric gauge theories and
topological strings, we study melting crystal, which is known as random plane
partition, from the viewpoint of integrable systems. We show that a series of
partition functions of melting crystals gives rise to a tau function of the
one-dimensional Toda hierarchy, where the models are defined by adding suitable
potentials, endowed with a series of coupling constants, to the standard
statistical weight. These potentials can be converted to a commutative
sub-algebra of quantum torus Lie algebra. This perspective reveals a remarkable
connection between random plane partition and quantum torus Lie algebra, and
substantially enables to prove the statement. Based on the result, we briefly
argue the integrable structures of five-dimensional
supersymmetric gauge theories and -model topological strings. The
aforementioned potentials correspond to gauge theory observables analogous to
the Wilson loops, and thereby the partition functions are translated in the
gauge theory to generating functions of their correlators. In topological
strings, we particularly comment on a possibility of topology change caused by
condensation of these observables, giving a simple example.Comment: Final version to be published in Commun. Math. Phys. . A new section
is added and devoted to Conclusion and discussion, where, in particular, a
possible relation with the generating function of the absolute Gromov-Witten
invariants on CP^1 is commented. Two references are added. Typos are
corrected. 32 pages. 4 figure
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