The Covariant Quantum Superstring and Superparticle from their Classical Actions

We develop an approach based on the Noether method to construct nilpotent BRST charges and BRST-invariant actions. We apply this approach first to the holomorphic part of the flat-space covariant superstring, and we find that the ghosts b, c_z which we introduced by hand in our earlier work, are needed to fix gauge symmetries of the ghost action. Then we apply this technique to the superparticle and determine its cohomology. Finally, we extend our results to the combined left- and right-moving sectors of the superstring.Comment: 14 pages, harmva

Harmonic Superspaces from Superstrings

We derive harmonic superspaces for N=2,3,4 SYM theory in four dimensions from superstring theory. The pure spinors in ten dimensions are dimensionally reduced and yield the harmonic coordinates. Two anticommuting BRST charges implement Grassmann analyticity and harmonic analyticity. The string field theory action produces the action and field equations for N=3 SYM theory in harmonic superspace.Comment: 14 pp. Harvma

N=4 Superconformal Symmetry for the Covariant Quantum Superstring

We extend our formulation of the covariant quantum superstring as a WZNW model with N=2 superconformal symmetry to N=4. The two anticommuting BRST charges in the N=4 multiplet of charges are the usual BRST charge Q_S and a charge Q_V proposed by Dijkgraaf, Verlinde and Verlinde for topological models. Using our recent work on "gauging cosets", we then construct a further charge Q_C which anticommutes with Q_S + Q_V and which is intended for the definition of the physical spectrum.Comment: LaTeX, 18 pages, no figure

Non-Critical Covariant Superstrings

We construct a covariant description of non-critical superstrings in even dimensions. We construct explicitly supersymmetric hybrid type variables in a linear dilaton background, and study an underlying N=2 twisted superconformal algebra structure. We find similarities between non-critical superstrings in 2n+2 dimensions and critical superstrings compactified on CY_(4-n) manifolds. We study the spectrum of the non-critical strings, and in particular the Ramond-Ramond massless fields. We use the supersymmetric variables to construct the non-critical superstrings sigma-model action in curved target space backgrounds with coupling to the Ramond-Ramond fields. We consider as an example non-critical type IIA strings on AdS_2 background with Ramond-Ramond 2-form flux.Comment: harvmac, amssym, 46 p

Aspects of Quantum Fermionic T-duality

We study two aspects of fermionic T-duality: the duality in purely fermionic sigma models exploring the possible obstructions and the extension of the T-duality beyond classical approximation. We consider fermionic sigma models as coset models of supergroups divided by their maximally bosonic subgroup OSp(m|n)/SO(m) x Sp(n). Using the non-abelian T-duality and a non-conventional gauge fixing we derive their fermionic T-duals. In the second part of the paper, we prove the conformal invariance of these models at one and two loops using the Background Field Method and we check the Ward Identities.Comment: 65 pages, 5 figure

The Background Field Method and the Linearization Problem for Poisson Manifolds

The background field method (BFM) for the Poisson Sigma Model (PSM) is studied as an example of the application of the BFM technique to open gauge algebras. The relationship with Seiberg-Witten maps arising in non-commutative gauge theories is clarified. It is shown that the implementation of the BFM for the PSM in the Batalin-Vilkovisky formalism is equivalent to the solution of a generalized linearization problem (in the formal sense) for Poisson structures in the presence of gauge fields. Sufficient conditions for the existence of a solution and a constructive method to derive it are presented.Comment: 33 pp. LaTex, references and comments adde

Curved Beta-Gamma Systems and Quantum Koszul Resolution

We consider the partition function of beta-gamma systems in curved space of the type discussed by Nekrasov and Witten. We show how the Koszul resolution theorem can be applied to the computation of the partition functions and to characters of these systems and find a prescription to enforce the hypotheses of the theorem at the path integral level. We illustrate the technique in a few examples: a simple 2-dimensional target space, the N-dimensional conifold, and a superconifold. Our method can also be applied to the Pure Spinor constraints of superstrings.Comment: harvmac, 17 page