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

Role of Short Distance Behavior in Off-Shell Open-String Field Theory

A recent proposal for a background independent open string field theory is studied in detail for a class of backgrounds that correspond to general quadratic boundary interactions on the world-sheet. A short-distance cut-off is introduced to formulate the theory with a finite number of local and potentially unrenormalizable boundary couplings. It is shown that renormalization of the boundary couplings makes both the world-sheet partition function and the string field action finite and cut-off independent, although the resulting string field action has an unpalatable dependence on the leading unrenormalizable coupling.Comment: 16 page

Categories of holomorphic line bundles on higher dimensional noncommutative complex tori

We construct explicitly noncommutative deformations of categories of holomorphic line bundles over higher dimensional tori. Our basic tools are Heisenberg modules over noncommutative tori and complex/holomorphic structures on them introduced by A. Schwarz. We obtain differential graded (DG) categories as full subcategories of curved DG categories of Heisenberg modules over the complex noncommutative tori. Also, we present the explicit composition formula of morphisms, which in fact depends on the noncommutativity.Comment: 28 page

Theta Dependence In The Large N Limit Of Four-Dimensional Gauge Theories

The theta dependent of pure gauge theories in four dimensions can be studied using a duality of large N gauge theories with string theory on a certain spacetime. Via this duality, one can argue that for every theta, there are infinitely many vacua that are stable in the large N limit. The true vacuum, found by minimizing the energy in this family, is a smooth function of theta except at theta equal to pi, where it jumps. This jump is associated with spontaneous breaking of CP symmetry. Domain walls separating adjacent vacua are described in terms of wrapped sixbranes.Comment: 8 p

Mirror Symmetry of Calabi-Yau Supermanifolds

We study super Landau-Ginzburg mirrors of the weighted projective superspace WCP^{3|2} which is a Calabi-Yau supermanifold and appeared in hep-th/0312171(Witten) in the topological B-model. One of them is an elliptic fibration over the complex plane whose coordinate is given in terms of two bosonic and two fermionic variables as well as Kahler parameter of WCP^{3|2}. The other is some patch of a degree 3 Calabi-Yau hypersurface in CP^2 fibered by the complex plane whose coordinate depends on both above four variables and Kahler parameter but its dependence behaves quite differently.Comment: 12pp; the last paragraph of section 1 improved and some clarifications adde

Loop Variables and Gauge Invariance in (Open) Bosonic String Theory

We give a simplified and more complete description of the loop variable approach for writing down gauge invariant equations of motion for the fields of the open string. A simple proof of gauge invariance to all orders is given. In terms of loop variables, the interacting equations look exactly like the free equations, but with a loop variable depending on an extra parameter, thus making it a band of finite width. The arguments for gauge invariance work exactly as in the free case. We show that these equations are Wilsonian RG equations with a finite world-sheet cutoff and that in the infrared limit, equivalence with the Callan-Symanzik $\beta$-functions should ensure that they reproduce the on-shell scattering amplitudes in string theory. It is applied to the tachyon-photon system and the general arguments for gauge invariance can be easily checked to the order calculated. One can see that when there is a finite world sheet cutoff in place, even the U(1) invariance of the equations for the photon, involves massive mode contributions. A field redefinition involving the tachyon is required to get the gauge transformations of the photon into standard form.Comment: 20 pages, Late

AdS/CFT and large-N volume independence

We study the Eguchi-Kawai reduction in the strong-coupling domain of gauge theories via the gravity dual of N=4 super-Yang-Mills on R^3xS^1. We show that D-branes geometrize volume independence in the center-symmetric vacuum and give supergravity predictions for the range of validity of reduced large-N models at strong coupling.Comment: 4 pages, 2 figures; references and comments adde

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

Background Fields in 2+1 Topological Gravity

The partition function of 2+1 Chern-Simons Witten topological gravity has an attractive interpretation in terms of the unbroken and broken phases of gravity. We make this physical interpretation manifest using the background field method.Comment: 10 pages, LaTeX, OUTP-93-03