On Type II strings in exact superconformal non-constant RR backgrounds

An explicitly exact superconformal description is provided to some classes of Type II string theories in non constant RR backgrounds. This is done by applying the manifest (2,2) approach of Berkovits and Maldacena to Type II strings and by studying the condition of exact conformal invariance of certain supersymmetric backgrounds. We find a new set of exact type IIA strings with non constant RR 2-form and 4-form curvatures and for type IIB with non constant 3-form curvature.Comment: 15 pages; typos and a reference adde

A Representation of Symmetry Generators for the Type IIB Superstring on a Plane Wave in the U(4) Formalism

We calculate the symmetry currents for the type IIB superstring on a maximally supersymmetric plane wave background using the N=(2,2) superconformally covariant U(4) formulation developed by Berkovits, Maldacena and Maoz. An explicit realization of the U(4) generators together with 16 fermionic generators is obtained in terms of the N=(2,2) worldsheet fields. Because the action is no longer quadratic, we use a light-cone version to display the currents in terms of the covariant worldsheet variables.Comment: 9 pages, harvmac, Corrected some typographical errors, Added reference

Algebraic-geometrical formulation of two-dimensional quantum gravity

We find a volume form on moduli space of double punctured Riemann surfaces whose integral satisfies the Painlev\'e I recursion relations of the genus expansion of the specific heat of 2D gravity. This allows us to express the asymptotic expansion of the specific heat as an integral on an infinite dimensional moduli space in the spirit of Friedan-Shenker approach. We outline a conjectural derivation of such recursion relations using the Duistermaat-Heckman theorem.Comment: 10 pages, Latex fil

Imaging memory in temporal lobe epilepsy: predicting the effects of temporal lobe resection

Functional magnetic resonance imaging can demonstrate the functional anatomy of cognitive processes. In patients with refractory temporal lobe epilepsy, evaluation of preoperative verbal and visual memory function is important as anterior temporal lobe resections may result in material specific memory impairment, typically verbal memory decline following left and visual memory decline after right anterior temporal lobe resection. This study aimed to investigate reorganization of memory functions in temporal lobe epilepsy and to determine whether preoperative memory functional magnetic resonance imaging may predict memory changes following anterior temporal lobe resection. We studied 72 patients with unilateral medial temporal lobe epilepsy (41 left) and 20 healthy controls. A functional magnetic resonance imaging memory encoding paradigm for pictures, words and faces was used testing verbal and visual memory in a single scanning session on a 3T magnetic resonance imaging scanner. Fifty-four patients subsequently underwent left (29) or right (25) anterior temporal lobe resection. Verbal and design learning were assessed before and 4 months after surgery. Event-related functional magnetic resonance imaging analysis revealed that in left temporal lobe epilepsy, greater left hippocampal activation for word encoding correlated with better verbal memory. In right temporal lobe epilepsy, greater right hippocampal activation for face encoding correlated with better visual memory. In left temporal lobe epilepsy, greater left than right anterior hippocampal activation on word encoding correlated with greater verbal memory decline after left anterior temporal lobe resection, while greater left than right posterior hippocampal activation correlated with better postoperative verbal memory outcome. In right temporal lobe epilepsy, greater right than left anterior hippocampal functional magnetic resonance imaging activation on face encoding predicted greater visual memory decline after right anterior temporal lobe resection, while greater right than left posterior hippocampal activation correlated with better visual memory outcome. Stepwise linear regression identified asymmetry of activation for encoding words and faces in the ipsilateral anterior medial temporal lobe as strongest predictors for postoperative verbal and visual memory decline. Activation asymmetry, language lateralization and performance on preoperative neuropsychological tests predicted clinically significant verbal memory decline in all patients who underwent left anterior temporal lobe resection, but were less able to predict visual memory decline after right anterior temporal lobe resection. Preoperative memory functional magnetic resonance imaging was the strongest predictor of verbal and visual memory decline following anterior temporal lobe resection. Preoperatively, verbal and visual memory function utilized the damaged, ipsilateral hippocampus and also the contralateral hippocampus. Memory function in the ipsilateral posterior hippocampus may contribute to better preservation of memory after surgery

Nonperturbative Relations in N=2 SUSY Yang-Mills and WDVV equation

We find the nonperturbative relation between $\langle {\rm tr} \phi^2 \rangle$, $\langle {\rm tr} \phi^3\rangle$ the prepotential ${\cal F}$ and the vevs $\langle \phi_i\rangle$ in $N=2$ supersymmetric Yang-Mills theories with gauge group $SU(3)$. Nonlinear differential equations for ${\cal F}$ including the Witten -- Dijkgraaf -- Verlinde -- Verlinde equation are obtained. This indicates that $N=2$ SYM theories are essentially topological field theories and that should be seen as low-energy limit of some topological string theory. Furthermore, we construct relevant modular invariant quantities, derive canonical relations between the periods and investigate the structure of the beta function by giving its explicit form in the moduli coordinates. In doing this we discuss the uniformization problem for the quantum moduli space. The method we propose can be generalized to $N=2$ supersymmetric Yang-Mills theories with higher rank gauge groups.Comment: 12 pages, LaTex. Expanded version. New results, corrections, references and acknowledgements adde

Mass Deformations of Super Yang-Mills Theories in D= 2+1, and Super-Membranes: A Note

Mass deformations of supersymmetric Yang-Mills theories in three spacetime dimensions are considered. The gluons of the theories are made massive by the inclusion of a non-local gauge and Poincare invariant mass term due to Alexanian and Nair, while the matter fields are given standard Gaussian mass-terms. It is shown that the dimensional reduction of such mass deformed gauge theories defined on $R^3$ or $R\times T^2$ produces matrix quantum mechanics with massive spectra. In particular, all known massive matrix quantum mechanical models obtained by the deformations of dimensional reductions of minimal super Yang-Mills theories in diverse dimensions are shown also to arise from the dimensional reductions of appropriate massive Yang-Mills theories in three spacetime dimensions. Explicit formulae for the gauge theory actions are provided.Comment: 20 Page

RG Flow Irreversibility, C-Theorem and Topological Nature of 4D N=2 SYM

We determine the exact beta function and a RG flow Lyapunov function for N=2 SYM with gauge group SU(n). It turns out that the classical discriminants of the Seiberg-Witten curves determine the RG potential. The radial irreversibility of the RG flow in the SU(2) case and the non-perturbative identity relating the $u$-modulus and the superconformal anomaly, indicate the existence of a four dimensional analogue of the c-theorem for N=2 SYM which we formulate for the full SU(n) theory. Our investigation provides further evidence of the essentially topological nature of the theory.Comment: 9 pages, LaTeX file. Discussion on WDVV and integrability. References added. Version published in PR

Irregular singularities in Liouville theory

Motivated by problems arising in the study of N=2 supersymmetric gauge theories we introduce and study irregular singularities in two-dimensional conformal field theory, here Liouville theory. Irregular singularities are associated to representations of the Virasoro algebra in which a subset of the annihilation part of the algebra act diagonally. In this paper we define natural bases for the space of conformal blocks in the presence of irregular singularities, describe how to calculate their series expansions, and how such conformal blocks can be constructed by some delicate limiting procedure from ordinary conformal blocks. This leads us to a proposal for the structure functions appearing in the decomposition of physical correlation functions with irregular singularities into conformal blocks. Taken together, we get a precise prediction for the partition functions of some Argyres-Douglas type theories on the four-sphere.Comment: 84 pages, 6 figure

Taming open/closed string duality with a Losev trick

A target space string field theory formulation for open and closed B-model is provided by giving a Batalin-Vilkovisky quantization of the holomorphic Chern-Simons theory with off-shell gravity background. The target space expression for the coefficients of the holomorphic anomaly equation for open strings are obtained. Furthermore, open/closed string duality is proved from a judicious integration over the open string fields. In particular, by restriction to the case of independence on continuous open moduli, the shift formulas of [7] are reproduced and shown therefore to encode the data of a closed string dual.Comment: 22 pages, no figures; v.2 Refs. and a comment added

On the Picard-Fuchs Equations for Massive N=2 Seiberg-Witten Theories

A new method to obtain the Picard-Fuchs equations of effective, N=2 supersymmetric gauge theories with massive matter hypermultiplets in the fundamental representation is presented. It generalises a previously described method to derive the Picard-Fuchs equations of both pure super Yang-Mills and supersymmetric gauge theories with massless matter hypermultiplets. The techniques developed are well suited to symbolic computer calculations.Comment: 29 pages, uses phyzzx.te