Symmetries and Observables for BF-theories in Superspace

The supersymmetric version of a topological quantum field theory describing flat connections, the super BF-theory, is studied in the superspace formalism. A set of observables related to topological invariants is derived from the curvature of the superspace. Analogously to the non-supersymmetric versions, the theory exhibits a vector-like supersymmetry. The role of the vector supersymmetry and an additional new symmetry of the action in the construction of observables is explained.Comment: 11 pages, LaTe

Chern-Simons Theory on S^1-Bundles: Abelianisation and q-deformed Yang-Mills Theory

We study Chern-Simons theory on 3-manifolds $M$ that are circle-bundles over 2-dimensional surfaces $\Sigma$ and show that the method of Abelianisation, previously employed for trivial bundles $\Sigma \times S^1$, can be adapted to this case. This reduces the non-Abelian theory on $M$ to a 2-dimensional Abelian theory on $\Sigma$ which we identify with q-deformed Yang-Mills theory, as anticipated by Vafa et al. We compare and contrast our results with those obtained by Beasley and Witten using the method of non-Abelian localisation, and determine the surgery and framing presecription implicit in this path integral evaluation. We also comment on the extension of these methods to BF theory and other generalisations.Comment: 37 pages; v2: references adde

Conformal Field Theory for the Superstring in a Ramond-Ramond Plane Wave Background

A quantizable worldsheet action is constructed for the superstring in a supersymmetric plane wave background with Ramond-Ramond flux. The action is manifestly invariant under all isometries of the background and is an exact worldsheet conformal field theory.Comment: 13 pages harvma

PP-wave and Non-supersymmetric Gauge Theory

We extend the pp-wave correspondence to a non supersymmetric example. The model is the type 0B string theory on the pp-wave R-R background. We explicitly solve the model and give the spectrum of physical states. The field theory counterpart is given by a sector of the large N SU(N) x SU(N) CFT living on a stack of N electric and N magnetic D3-branes. The relevant effective coupling constant is g_{eff}=g_sN/J^2. The string theory has a tachyon in the spectrum, whose light-cone energy can be exactly computed as a function of g_{eff}. We argue that the perturbative analysis in g_{eff} in the dual gauge theory is reliable, with corrections of non perturbative type. We find a precise state/operator map, showing that the first perturbative corrections to the anomalous dimensions of the operators have the behavior expected from the string analysis.Comment: 19 pages. Revised versio

Near-flat space limit and Einstein manifolds

We study the near-flat space limit for strings on AdS(5)xM(5), where the internal manifold M(5) is equipped with a generic metric with U(1)xU(1)xU(1) isometry. In the bosonic sector, the limiting sigma model is similar to the one found for AdS(5)xS(5), as the global symmetries are reduced in the most general case. When M(5) is a Sasaki-Einstein space like T(1,1), Y(p,q) and L(p,q,r), whose dual CFT's have N=1 supersymmetry, the near-flat space limit gives the same bosonic sector of the sigma model found for AdS(5)xS(5). This indicates the generic presence of integrable subsectors in AdS/CFT.Comment: 30 pages, 1 figur

Quantizing three-spin string solution in AdS_5 x S^5

As was recently found in hep-th/0304255, there exists a simple non-supersymmetric classical solution describing a closed string rotating in S^5 and located at the center of AdS_5. It is parametrized by the angular momentum J of the center of mass and two equal SO(6) angular momenta J' in the two other orthogonal rotation planes. The dual N=4 SYM operators should be scalar operators in SU(4) representations [0,J-J',2J'] or [J'-J,0,J'+J]. This solution is stable if J' > 3/2 J and for large J + 2 J' its classical energy admits an expansion in positive powers of g_eff = \lambda/(J + 2 J')^2: E= J + 2 J' + g_eff J' + ... . This suggests a possibility of a direct comparison with perturbative SYM results for the corresponding anomalous dimensions in the sector with g_eff << 1, by analogy with the BMN case. We conjecture that all quantum sigma model string corrections are then subleading at large J', so that the classical formula for the energy is effectively exact to all orders in \lambda. It could then be interpolated to weak coupling, representing a prediction for the anomalous dimensions on the SYM side. We test this conjecture by computing the 1-loop superstring sigma model correction to the classical energy.Comment: 25 pages, harvmac. v5: minor misprints in eqs (2.6),(2.16),(2.20),(2.21) correcte

Goedel, Penrose, anti-Mach: extra supersymmetries of time-dependent plane waves

We prove that M-theory plane waves with extra supersymmetries are necessarily homogeneous (but possibly time-dependent), and we show by explicit construction that such time-dependent plane waves can admit extra supersymmetries. To that end we study the Penrose limits of Goedel-like metrics, show that the Penrose limit of the M-theory Goedel metric (with 20 supercharges) is generically a time-dependent homogeneous plane wave of the anti-Mach type, and display the four extra Killings spinors in that case. We conclude with some general remarks on the Killing spinor equations for homogeneous plane waves.Comment: 20 pages, LaTeX2

N=(4,4) Type IIA String Theory on PP-Wave Background

We construct IIA GS superstring action on the ten-dimensional pp-wave background, which arises as the compactification of eleven-dimensional pp-wave geometry along the isometry direction. The background geometry has 24 Killing spinors and among them, 16 components correspond to the non-linearly realized kinematical supersymmetry in the string action. The remaining eight components are linearly realized and shown to be independent of x^+ coordinate, which is identified with the world-sheet time coordinate of the string action in the light-cone gauge. The resultant dynamical N=(4,4) supersymmetry is investigated, which is shown to be consistent with the field contents of the action containing two free massive supermultiplets.Comment: latex, 15 pages; v2: typos corrected, polished, references adde