1/4-BPS states on noncommutative tori

We give an explicit expression for classical 1/4-BPS fields in supersymmetric Yang-Mills theory on noncommutative tori. We use it to study quantum 1/4-BPS states. In particular we calculate the degeneracy of 1/4-BPS energy levels.Comment: 15 pages, Latex; v.2 typos correcte

On Asymptotic Hamiltonian for SU(N) Matrix Theory

We compute the leading contribution to the effective Hamiltonian of SU(N) matrix theory in the limit of large separation. We work with a gauge fixed Hamiltonian and use generalized Born-Oppenheimer approximation, extending the recent work of Halpern and Schwartz for SU(2). The answer turns out to be a free Hamiltonian for the coordinates along the flat directions of the potential. Applications to finding ground state candidates and calculation of the correction (surface) term to Witten index are discussed.Comment: 13 pages, Latex; v2: a reference added; v3: References to the papers by M.B. Green and M. Gutperle are added. The complete calculation of the Witten index for SU(N) matrix theory follows from combination of the results of our paper with the results of M.B. Green and M. Gutperle and the results obtained by G. Moore, N. Nekrasov, and S. Shatashvil

The Ground Ring of N=2 Minimal String Theory

We study the \NN=2 string theory or the \NN=4 topological string on the deformed CHS background. That is, we consider the \NN=2 minimal model coupled to the \NN=2 Liouville theory. This model describes holographically the topological sector of Little String Theory. We use degenerate vectors of the respective \NN=2 Verma modules to find the set of BRST cohomologies at ghost number zero--the ground ring, and exhibit its structure. Physical operators at ghost number one constitute a module of the ground ring, so the latter can be used to constrain the S-matrix of the theory. We also comment on the inequivalence of BRST cohomologies of the \NN=2 string theory in different pictures.Comment: 25 pages, latex, small correction

Moduli spaces of maximally supersymmetric solutions on noncommutative tori and noncommutative orbifolds

A maximally supersymmetric configuration of super Yang-Mills living on a noncommutative torus corresponds to a constant curvature connection. On a noncommutative toroidal orbifold there is an additional constraint that the connection be equivariant. We study moduli spaces of (equivariant) constant curvature connections on noncommutative even-dimensional tori and on toroidal orbifolds. As an illustration we work out the cases of Z_{2} and Z_{4} orbifolds in detail. The results we obtain agree with a commutative picture describing systems of branes wrapped on cycles of the torus and branes stuck at exceptional orbifold points.Comment: 21 pages, Late

g-function in perturbation theory

We present some explicit computations checking a particular form of gradient formula for a boundary beta function in two-dimensional quantum field theory on a disc. The form of the potential function and metric that we consider were introduced in hep-th/9210065, hep-th/9311177 in the context of background independent open string field theory. We check the gradient formula to the third order in perturbation theory around a fixed point. Special consideration is given to situations when resonant terms are present exhibiting logarithmic divergences and universal nonlinearities in beta functions. The gradient formula is found to work to the given order.Comment: 1+14 pages, Latex; v.2: typos corrected; v.3: minor corrections, to appear in IJM

Supergeometry and Arithmetic Geometry

We define a superspace over a ring $R$ as a functor on a subcategory of the category of supercommutative $R$-algebras. As an application the notion of a $p$-adic superspace is introduced and used to give a transparent construction of the Frobenius map on $p$-adic cohomology of a smooth projective variety over the ring of $p$-adic integers.Comment: 14 pages, expanded introduction, more detail

Unstable solitons on noncommutative tori and D-branes

We describe a class of exact solutions of super Yang-Mills theory on even-dimensional noncommutative tori. These solutions generalize the solitons on a noncommutative plane introduced in hep-th/0009142 that are conjectured to describe unstable D2p-D0 systems. We show that the spectrum of quadratic fluctuations around our solutions correctly reproduces the string spectrum of the D2p-D0 system in the Seiberg-Witten decoupling limit. In particular the fluctuations correctly reproduce the 0-0 string winding modes. For p=1 and p=2 we match the differences between the soliton energy and the energy of an appropriate SYM BPS state with the binding energies of D2-D0 and D4-D0 systems. We also give an example of a soliton that we conjecture describes branes of intermediate dimension on a torus such as a D2-D4 system on a four-torus.Comment: 22 pages, Latex; v.2: references adde