Electroweak Theory and Noncommutative Geometry

The noncommutative generalisation of the standard electroweak model due to Balakrishna, Gursey and Wali is formulated in terms of the derivations Der_2(M_3) of a three dimensional representation of the su(2) Lie algebra of weak isospin. A light Higgs boson of mass about 130 GeV, together with four very heavy scalar bosons are predicted.Comment: 11 pages, LATEX, no figures. Talk given at the 2nd Gursey Memorial Conference, June 2000, Istanbu

Scaling Cosmologies from Duality Twisted Compactifications

Oscillating moduli fields can support a cosmological scaling solution in the presence of a perfect fluid when the scalar field potential satisfies appropriate conditions. We examine when such conditions arise in higher-dimensional, non-linear sigma-models that are reduced to four dimensions under a generalized Scherk-Schwarz compactification. We show explicitly that scaling behaviour is possible when the higher-dimensional action exhibits a global SL(n,R) or O(2,2) symmetry. These underlying symmetries can be exploited to generate non-trivial scaling solutions when the moduli fields have non-canonical kinetic energy. We also consider the compactification of eleven-dimensional vacuum Einstein gravity on an elliptic twisted torus.Comment: 21 pages, 3 figure

Beta, Dipole and Noncommutative Deformations of M-theory Backgrounds with One or More Parameters

We construct new M-theory solutions starting from those that contain 5 U(1) isometries. We do this by reducing along one of the 5-torus directions, then T-dualizing via the action of an O(4,4) matrix and lifting back to 11-dimensions. The particular T-duality transformation is a sequence of O(2,2) transformations embedded in O(4,4), where the action of each O(2,2) gives a Lunin-Maldacena deformation in 10-dimensions. We find general formulas for the metric and 4-form field of single and multiparameter deformed solutions, when the 4-form of the initial 11-dimensional background has at most one leg along the 5-torus. All the deformation terms in the new solutions are given in terms of subdeterminants of a 5x5 matrix, which represents the metric on the 5-torus. We apply these results to several M-theory backgrounds of the type AdS_r x X^{11-r}. By appropriate choices of the T-duality and reduction directions we obtain analogues of beta, dipole and noncommutative deformations. We also provide formulas for backgrounds with only 3 or 4 U(1) isometries and study a case, for which our assumption for the 4-form field is violated.Comment: v2:minor corrections, v3:small improvements, v4:conclusions expanded, to appear in Class. Quant. Gra

Strings on the deformed T^{1,1}: giant magnon and single spike solutions

In this paper we find giant magnon and single spike string solutions in a sector of the gamma-deformed conifold. We examine the dispersion relations and find a behavior analogous to the undeformed case. The transcendental functional relations between the conserved charges are shifted by certain gamma-dependent term. The latter is proportional to the total momentum and thus qualitatively different from known cases.Comment: 35 pages, no figure

On the perturbative chiral ring for marginally deformed N=4 SYM theories

For \cal{N}=1 SU(N) SYM theories obtained as marginal deformations of the \cal{N}=4 parent theory we study perturbatively some sectors of the chiral ring in the weak coupling regime and for finite N. By exploiting the relation between the definition of chiral ring and the effective superpotential we develop a procedure which allows us to easily determine protected chiral operators up to n loops once the superpotential has been computed up to (n-1) order. In particular, for the Lunin-Maldacena beta-deformed theory we determine the quantum structure of a large class of operators up to three loops. We extend our procedure to more general Leigh-Strassler deformations whose chiral ring is not fully understood yet and determine the weight-two and weight-three sectors up to two loops. We use our results to infer general properties of the chiral ring.Comment: LaTex, 40 pages, 4 figures, uses JHEP3; v2: minor correction

A Massive S-duality in 4 dimensions

We reduce the Type IIA supergravity theory with a generalized Scherk-Schwarz ansatz that exploits the scaling symmetry of the dilaton, the metric and the NS 2-form field. The resulting theory is a new massive, gauged supergravity theory in four dimensions with a massive 2-form field and a massive 1-form field. We show that this theory is S-dual to a theory with a massive vector field and a massive 2-form field, which are dual to the massive 2-form and 1-form fields in the original theory, respectively. The S-dual theory is shown to arise from a Scherk-Schwarz reduction of the heterotic theory. Hence we establish a massive, S-duality type relation between the IIA theory and the heterotic theory in four dimensions. We also show that the Lagrangian for the new four dimensional theory can be put in the most general form of a D=4, N=4 gauged Lagrangian found by Schon and Weidner, in which (part of) the SL(2) group has been gauged.Comment: 20 pages, references adde

Semi-classical Strings in Sasaki-Einstein Manifolds

We find point-like and classical string solutions on the AdS_5 x X^5, where X^5 are the 5-dimensional Sasaki-Einstein manifolds Ypq and Lpqr. The number of acceptable solutions is limited drastically in order to satisfy the constraints on the parameters and coordinates of the manifolds. The energy of the solutions depends on the parameters of the Sasaki-Einstein manifolds and on the conserved momenta transcendentally. A discussion on BPS solutions is presented as well.Comment: 34 pages, 9 figure

Lectures on Nongeometric Flux Compactifications

These notes present a pedagogical review of nongeometric flux compactifications. We begin by reviewing well-known geometric flux compactifications in Type II string theory, and argue that one must include nongeometric "fluxes" in order to have a superpotential which is invariant under T-duality. Additionally, we discuss some elementary aspects of the worldsheet description of nongeometric backgrounds. This review is based on lectures given at the 2007 RTN Winter School at CERN.Comment: 31 pages, JHEP

Probing Universality in the Gravity Duals of N=1 SYM by gamma-deformations

Recently, a one-parameter deformation of the Maldacena-Nunez dual of the N=1 SYM theory was constructed in hep-th/0505100. According to the Lunin-Maldacena conjecture, the background is dual to pure N=1 SYM in the IR coupled to a KK sector whose dynamics is altered by a dipole deformation that is proportional to the deformation parameter gamma. Thus, the deformation serves to identify the aspects of the gravity backgrounds that bear the effects of the KK sector, hence non-universal in the dual gauge theory. We make this idea concrete by studying a Penrose limit of the deformed MN theory. We obtain an exactly solvable pp-wave that is conjectured to describe the IR dynamics of KK-hadrons in the field theory. The spectrum, the thermal partition function and the Hagedorn temperature are calculated. The Hagedorn temperature turns out to be independent of the deformation parameter.Comment: 29 pages, 1 figure, refs. added, typos corrected, v3: discussion extended and modified v4: discussion section modified, typos corrceted, v5: referencing correcte