Beta functions of topologically massive supergravity

We compute the one-loop beta functions of the cosmological constant, Newton's constant and the topological mass in topologically massive supergravity in three dimensions. We use a variant of the proper time method supplemented by a simple choice of cutoff function. We also employ two different analytic continuations of AdS3 and consider harmonic expansions on the 3-sphere as well as a 3-hyperboloid, and then show that they give the same results for the beta functions. We find that the dimensionless coefficient of the Chern-Simons term, 28, has vanishing beta function. The flow of the cosmological constant and Newton's constant depends on 28; we study analytically the structure of the flow and its fixed points in the limits of small and large ?. Open Access, \ua9 2014 The Authors

On M-Theory Embedding of Topologically Massive Gravity

We show that topologically massive gravity can be obtained by the consistent Kaluza-Klein reduction from recently constructed seven-dimensional gravity with topological terms. The internal four-manifold should be Einstein with the Pontryagin four-form constantly proportional to the volume form. We also discuss the possible lift of the system to D=11. This enables us to connect the mass parameter \tilde\mu in D=3 to the M5-brane charge. The dimensionless quantity 3/(G\tilde \mu) is discrete and proportional to N, where N is the number of M5-branes.Comment: 8 pages, no figures, references added, version appeared in Int.J.Mod.Phys.

D2-brane Chern-Simons theories: F-maximization = a-maximization

We study a system of N D2-branes probing a generic Calabi-Yau three-fold singularity in the presence of a non-zero quantized Romans mass n. We argue that the low-energy effective N = 2 Chern-Simons quiver gauge theory flows to a superconformal fixed point in the IR, and construct the dual AdS_4 solution in massive IIA supergravity. We compute the free energy F of the gauge theory on S^3 using localization. In the large N limit we find F = c(nN)^{1/3}a^{2/3}, where c is a universal constant and a is the a-function of the "parent" four-dimensional N = 1 theory on N D3-branes probing the same Calabi-Yau singularity. It follows that maximizing F over the space of admissible R-symmetries is equivalent to maximizing a for this class of theories. Moreover, we show that the gauge theory result precisely matches the holographic free energy of the supergravity solution, and provide a similar matching of the VEV of a BPS Wilson loop operator.Comment: 19 pages; v2: minor correction

The Revival of (0,2) Linear Sigma Models

Compactifications of the heterotic string are a viable route to phenomenologically realistic vacua and interesting new mathematics. While supergravity aspects of heterotic compactifications are largely well-understood their worldsheet description remains largely unexplored. We review recent work in developing linear sigma model techniques aimed at elucidating the underlying worldsheet description.Comment: Invited review for IJMPA. 53 page

Worldsheet Descriptions of Wrapped NS Five-Branes

We provide a world-sheet description of Neveu-Schwarz five-branes wrapped on a complex projective space. It is an orbifold of the product of an N=2 minimal model and the IR fixed point of a certain linear sigma model. We show how the naked singularity in the supergravity description is resolved by the world-sheet CFT. Applying mirror symmetry, we show that the low-energy theory of NS5-branes wrapped on CP^1 in Eguchi-Hanson space is described by the Seiberg-Witten prepotential for N=2 super-Yang-Mills, with the gauge group given by the ADE-type of the five-brane. The world-sheet CFT is generically regular, but singularities develop precisely at the Argyres-Douglas points and massless monopole points of the space-time theory. We also study the low-energy theory of NS5-branes wrapped on CP^2 in a Calabi-Yau 3-fold and its relation to (2,2) super-Yang-Mills theory in two dimensions.Comment: 40 pages, late

Ricci-Flat Branes

Up to overall harmonic factors, the D8-brane solution of the massive type IIA supergravity theory is the product of nine-dimensional Minkowski space (the worldvolume) with the real line (the transverse space). We show that the equations of motion allow for the worldvolume metric to be generalised to an arbitrary Ricci-flat one. If this nine-dimensional Ricci-flat manifold admits Killing spinors, then the resulting solutions are supersymmetric and satisfy the usual Bogomol'nyi bound, although they preserve fewer than the usual one half of the supersymmetries. We describe the possible choices of such manifolds, elaborating on the connection between the existence of Killing spinors and the self-duality condition on the curvature two-form. Since the D8-brane is a domain wall in ten dimensions, we are led to consider the general case: domain walls in any supergravity theory. Similar considerations hold here also. Moreover, it is shown that the worldvolume of any magnetic brane --- of which the domain walls are a specific example --- can be generalised in precisely the same way. The general class of supersymmetric solutions have gravitational instantons as their spatial sections. Some mention is made of the worldvolume solitons of such branes.Comment: 26 pages, LaTe

Comments on the String dual to N=1 SQCD

We study the String dual to N=1 SQCD deformed by a quartic superpotential in the quark superfields. We present a unified view of the previous results in the literature and find new exact solutions and new asymptotic solutions. Then we study the Physics encoded in these backgrounds, giving among other things a resolution to an old puzzle related to the beta function and a sufficient criteria for screening. We also extend our results to the SO(Nc) case where we present a candidate for the Wilson loop in the spinorial representation. Various aspects of this line of research are critically analyzed.Comment: 50 pages plus appendixes. Three figures and two table

The chiral anomaly from M theory

We argue that the chiral anomaly of \Ncal = 1 super Yang-Mills theory admits a dual description as spontaneous symmetry breaking in M theory on $G_2$ holonomy manifolds. We identify an angle of the $G_2$ background dual to the anomalous $U(1)_R$ current in field theory. This angle is not an isometry of the metric and we therefore develop a theory of ``massive isometry'' to describe fluctuations about such angles. Another example of a massive isometry occurs in the Atiyah-Hitchin metric.Comment: 1 + 44 pages. LaTe

N=2 Supersymmetric RG Flows and the IIB Dilaton

We show that there is a non-trivial relationship between the dilaton of IIB supergravity, and the coset of scalar fields in five-dimensional, gauged N=8 supergravity. This has important consequences for the running of the gauge coupling in massive perturbations of the AdS/CFT correspondence. We conjecture an exact analytic expression for the ten-dimensional dilaton in terms of five-dimensional quantities, and we test this conjecture. Specifically, we construct a family of solutions to IIB supergravity that preserve half of the supersymmetries, and are lifts of supersymmetric flows in five-dimensional, gauged N=8 supergravity. Via the AdS/CFT correspondence these flows correspond to softly broken N=4, large N Yang-Mills theory on part of the Coulomb branch of N=2 supersymmetric Yang-Mills. Our solutions involve non-trivial backgrounds for all the tensor gauge fields as well as for the dilaton and axion.Comment: 25 pages, 1 figure, harvmac, references adde