Stable Non-BPS States and Their Holographic Duals

Stable non-BPS states can be constructed and studied in a variety of contexts in string theory. Here we review some interesting constructions that arise from suspended and wrapped branes. We also exhibit some stable non-BPS states that have holographic duals.Comment: 10 pages, LaTeX, 10 .eps figures (included); based on a talk given at Strings 2000, Michiga

Open-String Actions and Noncommutativity Beyond the Large-B Limit

In the limit of large, constant B-field (the ``Seiberg-Witten limit''), the derivative expansion for open-superstring effective actions is naturally expressed in terms of the symmetric products *n. Here, we investigate corrections around the large-B limit, for Chern-Simons couplings on the brane and to quadratic order in gauge fields. We perform a boundary-state computation in the commutative theory, and compare it with the corresponding computation on the noncommutative side. These results are then used to examine the possible role of Wilson lines beyond the Seiberg-Witten limit. To quadratic order in fields, the entire tree-level amplitude is described by a metric-dependent deformation of the *2 product, which can be interpreted in terms of a deformed (non-associative) version of the Moyal * product.Comment: 30 pages, harvma

Towards an explicit expression of the Seiberg-Witten map at all orders

The Seiberg-Witten map links noncommutative gauge theories to ordinary gauge theories, and allows to express the noncommutative variables in terms of the commutative ones. Its explicit form can be found order by order in the noncommutative parameter theta and the gauge potential A by the requirement that gauge orbits are mapped on gauge orbits. This of course leaves ambiguities, corresponding to gauge transformations, and there is an infinity of solutions. Is there one better, clearer than the others ? In the abelian case, we were able to find a solution, linked by a gauge transformation to already known formulas, which has the property of admitting a recursive formulation, uncovering some pattern in the map. In the special case of a pure gauge, both abelian and non-abelian, these expressions can be summed up, and the transformation is expressed using the parametrisation in terms of the gauge group.Comment: 17 pages. Latex, 1 figure. v2: minor changes, published versio

Topological Chern-Simons Sigma Model

We consider topological twisting of recently constructed Chern-Simons-matter theories in three dimensions with N=4 or higher supersymmetry. We enumerate physically inequivalent twistings for each N, and find two different twistings for N=4, one for N=5,6, and four for N=8. We construct the two types of N=4 topological theories, which we call A/B-models, in full detail. The A-model has been recently studied by Kapustin and Saulina. The B-model is new and it consists solely of a Chern-Simons term of a complex gauge field up to BRST-exact terms. We also compare the new theories with topological Yang-Mills theories and find some interesting connections. In particular, the A-model seems to offer a new perspective on Casson invariant and its relation to Rozansky-Witten theory.Comment: 31 pages, no figure; v2. references adde

Noncritical String Correlators, Finite-N Matrix Models and the Vortex Condensate

We carry out a systematic study of correlation functions of momentum modes in the Euclidean c=1 string, as a function of the radius and to all orders in perturbation theory. We obtain simple explicit expressions for several classes of correlators in terms of special functions. The Normal Matrix Model is found to be a powerful calculational tool that computes c=1 string correlators even at finite N. This enables us to obtain a simple combinatoric formula for the 2n-point function of unit momentum modes, which after T-duality determines the vortex condensate. We comment on possible applications of our results to T-duality at c=1 and to the 2d black hole/vortex condensate problem.Comment: 38 pages, LaTe

Exactly stable non-BPS spinors in heterotic string theory on tori

Considering SO(32) heterotic string theory compactified on a torus of dimension 4 and less, stability of non-supersymmetric states is studied. A non-supersymmetric state with robust stability is constructed, and its exact stability is proven in a large region of moduli space against all the possible decay mechanisms allowed by charge conservation. Using various T-duality transform matrices, we translate various selection rules about conserved charges into simpler problems resembling partition and parity of integers. For heterotic string on T^4, we give a complete list of BPS atoms with elementary excitations, and we study BPS and non-BPS molecules with various binding energies. Using string-string duality, the results are interpreted in terms of Dirichlet-branes in type IIA string theory compactified on an orbifold limit of a K3 surface.Comment: 47 pages, 14 figures, LaTe

Hodge Duality Operation And Its Physical Applications On Supermanifolds

An appropriate definition of the Hodge duality $\star$ operation on any arbitrary dimensional supermanifold has been a long-standing problem. We define a working rule for the Hodge duality $\star$ operation on the $(2 + 2)$-dimensional supermanifold parametrized by a couple of even (bosonic) spacetime variables $x^\mu (\mu = 0, 1)$ and a couple of Grassmannian (odd) variables $\theta$ and $\bar\theta$ of the Grassmann algebra. The Minkowski spacetime manifold, hidden in the supermanifold and parametrized by $x^\mu (\mu = 0, 1)$, is chosen to be a flat manifold on which a two $(1 + 1)$-dimensional (2D) free Abelian gauge theory, taken as a prototype field theoretical model, is defined. We demonstrate the applications of the above definition (and its further generalization) for the discussion of the (anti-)co-BRST symmetries that exist for the field theoretical models of 2D- (and 4D) free Abelian gauge theories considered on the four $(2 + 2)$- (and six $(4 + 2)$)-dimensional supermanifolds, respectively.Comment: LaTeX file, 25 pages, Journal-versio

A Monopole Solution in open String Theory

We investigate a solution of the Weyl invariance conditions in open string theory in 4 dimensions. In the closed string sector this solution is a combination of the SU(2) Wess--Zumino--Witten model and a Liouville theory. The investigation is carried out in the $\sigma$ model approach where we have coupled all massless modes (especially an abelian gauge field via the boundary) and tachyon fields. Neglecting all higher derivatives in the field strength we get an exact result which can be interpreted as a monopole configuration living in non--trivial space time. The masses of both tachyon fields are quantized by $c_{wzw}$ and vanish for $c_{wzw} = 1$.Comment: 14 pages, Latex, DESY 93-15

Non-Commutative Instantons and the Seiberg-Witten Map

We present several results concerning non-commutative instantons and the Seiberg-Witten map. Using a simple ansatz we find a large new class of instanton solutions in arbitrary even dimensional non-commutative Yang-Mills theory. These include the two dimensional ``shift operator'' solutions and the four dimensional Nekrasov-Schwarz instantons as special cases. We also study how the Seiberg-Witten map acts on these instanton solutions. The infinitesimal Seiberg-Witten map is shown to take a very simple form in operator language, and this result is used to give a commutative description of non-commutative instantons. The instanton is found to be singular in commutative variables.Comment: 26 pages, AMS-LaTeX. v2: the formula for the commutative description of the Nekrasov-Schwarz instanton corrected (sec. 4). v3: minor correction

Ultra-violet Behavior of Bosonic Quantum Membranes

We treat the action for a bosonic membrane as a sigma model, and then compute quantum corrections by integrating out higher membrane modes. As in string theory, where the equations of motion of Einstein's theory emerges by setting $\beta = 0$, we find that, with certain assumptions, we can recover the equations of motion for the background fields. Although the membrane theory is non-renormalizable on the world volume by power counting, the investigation of the ultra-violet behavior of membranes may give us insight into the supersymmetric case, where we hope to obtain higher order M-theory corrections to 11 dimensional supergravity.Comment: 25 pages, Latex, no figure