From Marginal Deformations to Confinement

We consider type IIB supergravity backgrounds which describe marginal deformations of the Coulomb branch of N=4 super Yang-Mills theory with SO(4) x SO(2) global symmetry. Wilson loop calculations indicate that certain deformations enhance the Coulombic attraction between quarks and anti-quarks at the UV conformal fixed-point. In the IR region, these deformations can induce a transition to linear confinement.Comment: 14 pages, 4 figures, minor corrections, comments and references adde

NS5-Branes, T-Duality and Worldsheet Instantons

The equivalence of NS5-branes and ALF spaces under T-duality is well known. However, a naive application of T-duality transforms the ALF space into a smeared NS5-brane, de-localized on the dual, transverse, circle. In this paper we re-examine this duality, starting from a two-dimensional N=(4,4) gauged linear sigma model describing Taub-NUT space. After dualizing the circle fiber, we find that the smeared NS5-brane target space metric receives corrections from multi-worldsheet instantons. These instantons are identified as Nielsen-Olesen vortices. We show that their effect is to break the isometry of the target space, localizing the NS5-brane at a point. The contribution from the k-instanton sector is shown to be proportional to the weighted integral of the Euler form over the k-vortex moduli space. The duality also predicts the, previously unknown, asymptotic exponential decay coefficient of the BPS vortex solution.Comment: 26 pages. v2: Fourier modes of multi-vortex fermion zero mode corrected. Reference added. v3: typo correcte

Moduli Dynamics of AdS_3 Strings

We construct a general class of solutions for a classical string in AdS_3 spacetime. The construction is based on a Pohlmeyer type reduction, with the sinh-Gordon model providing the general N-soliton solutions. The corresponding exact spiky string configurations are then reconstructed through the inverse scattering method. It is shown that the string moduli are determined entirely by those of the solitons.Comment: 22 pages, no figures; references adde

Non-linear Dynamics in QED_3 and Non-trivial Infrared Structure

In this work we consider a coupled system of Schwinger-Dyson equations for self-energy and vertex functions in QED_3. Using the concept of a semi-amputated vertex function, we manage to decouple the vertex equation and transform it in the infrared into a non-linear differential equation of Emden-Fowler type. Its solution suggests the following picture: in the absence of infrared cut-offs there is only a trivial infrared fixed-point structure in the theory. However, the presence of masses, for either fermions or photons, changes the situation drastically, leading to a mass-dependent non-trivial infrared fixed point. In this picture a dynamical mass for the fermions is found to be generated consistently. The non-linearity of the equations gives rise to highly non-trivial constraints among the mass and effective (`running') gauge coupling, which impose lower and upper bounds on the latter for dynamical mass generation to occur. Possible implications of this to the theory of high-temperature superconductivity are briefly discussed.Comment: 29 pages LATEX, 7 eps figures incorporated, uses axodraw style. Discussion on the massless case (section 2) modified; no effect on conclusions, typos correcte

D3-branes on the Coulomb branch and instantons

The relative coefficients of higher derivative interactions of the IIB effective action of the form C^4, (D F_5)^4, F_5^8, ... (where C is the Weyl tensor and F_5 is the five-form field strength) are motivated by supersymmetry arguments. It is shown that the classical supergravity solution for N parallel D3-branes is unaltered by this combination of terms. The non-vanishing of \zeroC^2 in this background (where \zero C is the background value of the Weyl tensor) leads to effective O(1/alpha') interactions, such as C^2 and Lambda^8 (where Lambda is the dilatino). These contain D-instanton contributions in addition to tree and one-loop terms. The near horizon limit of the N D3-brane system describes a multi-AdS_5xS^5 geometry that is dual to \calN=4 SU(N) Yang-Mills theory spontaneously broken to S(U(M_1)x...xU(M_r)). Here, the N D3-branes are grouped into r coincident bunches with M_r in each group, with M_r/N = m_r fixed as N goes to infinity. The boundary correlation function of eight Lambda's is constructed explicitly. The second part of the paper considers effects of a constrained instanton in this large-N Yang-Mills theory by an extension of the analysis of Dorey, Hollowood and Khoze of the one-instanton measure at finite N. This makes precise the correspondence with the supergravity D-instanton measure at leading order in the 1/N expansion. However, the duality between instanton-induced correlation functions in Yang-Mills theory and the dual supergravity is somewhat obscured by complications relating to the structure of constrained instantons.Comment: 30 pages, JHEP style. Typos corrected and minor clarifications adde

Giants and loops in beta-deformed theories

We study extended objects in the gravity dual of the N=1 beta-deformation of N=4 Super Yang-Mills theory. We identify probe brane configurations corresponding to giant gravitons and Wilson loops. In particular we identify a new class of objects, given by D5-branes wrapped on a two-torus with a world-volume gauge field strength turned on along the torus. These appear when the deformation parameter assumes a rational value and the gauge theory spectrum has additional branches of vacua. We give an interpretation of the new D5-brane dual giant gravitons in terms of rotating vacuum expectation values in these additional branches.Comment: 26 pages; typos corrected, published versio

Instanton test of non-supersymmetric deformations of the AdS_5 x S^5

We consider instanton effects in a non-supersymmetric gauge theory obtained by marginal deformations of the N=4 SYM. This gauge theory is expected to be dual to type IIB string theory on the AdS_5 times deformed-S^5 background. From an instanton calculation in the deformed gauge theory we extract the prediction for the dilaton-axion field \tau in dual string theory. In the limit of small deformations where the supergravity regime is valid, our instanton result reproduces the expression for \tau of the supergravity solution found by Frolov.Comment: 15 page

A Connection between Twistors and Superstring Sigma Models on Coset Superspaces

We consider superstring sigma models that are based on coset superspaces G/H in which H arises as the fixed point set of an order-4 automorphism of G. We show by means of twistor theory that the corresponding first-order system, consisting of the Maurer-Cartan equations and the equations of motion, arises from a dimensional reduction of some generalised self-dual Yang-Mills equations in eight dimensions. Such a relationship might help shed light on the explicit construction of solutions to the superstring equations including their hidden symmetry structures and thus on the properties of their gauge theory duals.Comment: v3: 16 pages, typos fixed and minor clarifications adde

Double Scaling Limits in Gauge Theories and Matrix Models

We show that $\N=1$ gauge theories with an adjoint chiral multiplet admit a wide class of large-N double-scaling limits where $N$ is taken to infinity in a way coordinated with a tuning of the bare superpotential. The tuning is such that the theory is near an Argyres-Douglas-type singularity where a set of non-local dibaryons becomes massless in conjunction with a set of confining strings becoming tensionless. The doubly-scaled theory consists of two decoupled sectors, one whose spectrum and interactions follow the usual large-N scaling whilst the other has light states of fixed mass in the large-N limit which subvert the usual large-N scaling and lead to an interacting theory in the limit. $F$-term properties of this interacting sector can be calculated using a Dijkgraaf-Vafa matrix model and in this context the double-scaling limit is precisely the kind investigated in the "old matrix model'' to describe two-dimensional gravity coupled to $c<1$ conformal field theories. In particular, the old matrix model double-scaling limit describes a sector of a gauge theory with a mass gap and light meson-like composite states, the approximate Goldstone boson of superconformal invariance, with a mass which is fixed in the double-scaling limit. Consequently, the gravitational $F$-terms in these cases satisfy the string equation of the KdV hierarchy.Comment: 38 pages, 1 figure, reference adde

N=1* in 5 dimensions: Dijkgraaf-Vafa meets Polchinski-Strassler

One of the powerful techniques to analyze the 5 dimensional Super Yang Mills theory with a massive hypermultiplet (N=1*) is provided by the AdS/CFT correspondence. It predicts that, for certain special values of the hypermultiplet mass, this theory develops nonperturbative branches of the moduli space as well as new light degrees of freedom. We use the higher dimensional generalization of the matrix model/gauge theory correspondence and recover all the prediction of the supergravity analysis. We construct the map between the four dimensional holomorphic superpotential and the five dimensional action and explicitly show that the superpotential is flat along the nonperturbative branches. This is the first instance in which the Dijkgraaf-Vafa method is used to analyze intrinsically higher dimensional phenomena.Comment: 28 pages, Late