D-branes on Orbifolds with Discrete Torsion And Topological Obstruction

We find the orbifold analog of the topological relation recently found by Freed and Witten which restricts the allowed D-brane configurations of Type II vacua with a topologically non-trivial flat $B$-field. The result relies in Douglas proposal -- which we derive from worldsheet consistency conditions -- of embedding projective representations on open string Chan-Paton factors when considering orbifolds with discrete torsion. The orbifold action on open strings gives a natural definition of the algebraic K-theory group -- using twisted cross products -- responsible for measuring Ramond-Ramond charges in orbifolds with discrete torsion. We show that the correspondence between fractional branes and Ramond-Ramond fields follows in an interesting fashion from the way that discrete torsion is implemented on open and closed strings.Comment: 16 pages, harvmac, clarification regarding relation with torsion in homolog

Mirror Symmetry And Loop Operators

Wilson loops in gauge theories pose a fundamental challenge for dualities. Wilson loops are labeled by a representation of the gauge group and should map under duality to loop operators labeled by the same data, yet generically, dual theories have completely different gauge groups. In this paper we resolve this conundrum for three dimensional mirror symmetry. We show that Wilson loops are exchanged under mirror symmetry with Vortex loop operators, whose microscopic definition in terms of a supersymmetric quantum mechanics coupled to the theory encode in a non-trivial way a representation of the original gauge group, despite that the gauge groups of mirror theories can be radically different. Our predictions for the mirror map, which we derive guided by branes in string theory, are confirmed by the computation of the exact expectation value of Wilson and Vortex loop operators on the three-sphere.Comment: 92 pages, v2: minor clarifications in the introduction, to be published in JHE

Nonrelativistic closed string theory

We construct a Galilean invariant nongravitational closed string theory whose excitations satisfy a nonrelativistic dispersion relation. This theory can be obtained by taking a consistent low energy limit of any of the conventional string theories, including the heterotic string. We give a finite first order worldsheet Hamiltonian for this theory and show that this string theory has a sensible perturbative expansion, interesting high energy behavior of scattering amplitudes and a Hagedorn transition of the thermal ensemble. The strong coupling duals of the Galilean superstring theories are considered and are shown to be described by an eleven-dimensional Galilean invariant theory of light membrane fluctuations. A new class of Galilean invariant nongravitational theories of light-brane excitations are obtained. We exhibit dual formulations of the strong coupling limits of these Galilean invariant theories and show that they exhibit many of the conventional dualities of M theory in a nonrelativistic setting

D=2+1 N=2 Yang-Mills Theory From Wrapped Branes

We find a new solution of Type IIB supergravity which represents a collection of D5 branes wrapped on the topologically non-trivial S^3 of the deformed conifold geometry T^*S^3. The Type IIB solution is obtained by lifting a new solution of D=7 SU(2)_L x SU(2)_R gauged supergravity to ten dimensions in which SU(2)_D gauge fields in the diagonal subgroup are turned on. The supergravity solution describes a slice of the Coulomb branch in the large N limit of N=2 SYM in three dimensions.Comment: 19 pages, 1figure, harvmac; expanded analysis of D=4 N=2 system in the appendix, references adde