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

Cubic String Field Theory in pp-wave Background and Background Independent Moyal Structure

We study Witten open string field theory in the pp-wave background in the tensionless limit, and construct the N-string vertex in the basis which diagonalizes the string perturbative spectrum. We found that the Witten *-product can be viewed as infinite copies of the Moyal product with the same noncommutativity parameter $\theta=2$. Moreover, we show that this Moyal structure is universal in the sense that, written in the string bit basis, Witten's *-product for any background can always be given in terms of the above-mentioned Moyal structure. We identify some projective operators in this algebra that we argue to correspond to D-branes of the theory.Comment: Latex, 23 pages, reference adde

Electrified BPS Giants: BPS configurations on Giant Gravitons with Static Electric Field

We consider D3-brane action in the maximally supersymmetric type IIB plane-wave background. Upon fixing the light-cone gauge, we obtain the light-cone Hamiltonian which is manifestly supersymmetric. The 1/2 BPS solutions of this theory (solutions which preserve 16 supercharges) are either of the form of spherical three branes, the giant gravitons, or zero size point like branes. We then construct specific classes of 1/4 BPS solutions of this theory in which static electric field on the brane is turned on. These solutions are deformations about either of the two 1/2 BPS solutions. In particular, we study in some detail 1/4 BPS configurations with electric dipole on the three sphere giant, i.e. BIons on the giant gravitons, which we hence call BIGGons. We also study BPS configurations corresponding to turning on a background uniform constant electric field. As a result of this background electric field the three sphere giant is deformed to squashed sphere, while the zero size point like branes turn into circular or straight fundamental strings in the plane-wave background, with their tension equal to the background electric field.Comment: 32 pages, 1 eps figure; v2: Presentation of derivation of light-cone Hamiltonian improved, Refs adde

Light--like Wilson loops and gauge invariance of Yang--Mills theory in 1+1 dimensions

A light-like Wilson loop is computed in perturbation theory up to ${\cal O} (g^4)$ for pure Yang--Mills theory in 1+1 dimensions, using Feynman and light--cone gauges to check its gauge invariance. After dimensional regularization in intermediate steps, a finite gauge invariant result is obtained, which however does not exhibit abelian exponentiation. Our result is at variance with the common belief that pure Yang--Mills theory is free in 1+1 dimensions, apart perhaps from topological effects.Comment: 10 pages, plain TeX, DFPD 94/TH/

Worldsheet Scattering in AdS_5 x S^5

We calculate the S-matrix in the gauge-fixed sigma-model on AdS_5 x S^5 to the leading order in perturbation theory, and analyze how supersymmetry is realized on the scattering states. A mild nonlocality of the supercharges implies that their action on multi-particle states does not follow the Leibniz rule, which is replaced by a nontrivial coproduct. The plane wave symmetry algebra is thus naturally enhanced to a Hopf algebra. The scattering matrix elements obey the classical Yang-Baxter equation modified by the existence of the coproduct. This structure mirrors that of the large 't Hooft coupling expansion of the S-matrix for the spin chain in the dual super-Yang-Mills theory.Comment: 51 pages, v2: references added, v3: sign in (2.12), (6.19) and (6.21) corrected; v4: discussion of classical YBE is considerably modifie

Quantum Field Theories on Manifolds with Curved Boundaries: Scalar Fields

A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed Dirichlet and Neumann boundary conditions. The method is applied to a general renormalisable scalar field theory in four dimensions using dimensional regularisation to two loops and expanding about arbitrary background fields. Detailed results are also specialised to an $O(n)$ symmetric model with a single coupling constant. Extra boundary terms are introduced into the action which give rise to either Dirichlet or generalised Neumann boundary conditions for the quantum fields. For plane boundaries the resulting renormalisation group functions are in accord with earlier results but here the additional terms depending on the extrinsic curvature of the boundary are found. Various consistency relations are also checked and the implications of conformal invariance at the critical point where the $\beta$ function vanishes are also derived. The local Scr\"odinger equation for the wave functional defined by the functional integral under deformations of the boundary is also verified to two loops. Its consistency with the renormalisation group to all orders in perturbation theory is discussed.Comment: 50 pages, DAMTP/92-3

A Monte-Carlo study of the AdS/CFT correspondence: an exploration of quantum gravity effects

In this paper we study the AdS/CFT correspondence for N=4 SYM with gauge group U(N), compactified on S^3 in four dimensions using Monte-Carlo techniques. The simulation is based on a particular reduction of degrees of freedom to commuting matrices of constant fields, and in particular, we can write the wave functions of these degrees of freedom exactly. The square of the wave function is equivalent to a probability density for a Boltzman gas of interacting particles in six dimensions. From the simulation we can extract the density particle distribution for each wave function, and this distribution can be interpreted as a special geometric locus in the gravitational dual. Studying the wave functions associated to half-BPS giant gravitons, we are able to show that the matrix model can measure the Planck scale directly. We also show that the output of our simulation seems to match various theoretical expectations in the large N limit and that it captures 1/N effects as statistical fluctuations of the Boltzman gas with the expected scaling. Our results suggest that this is a very promising approach to explore quantum corrections and effects in gravitational physics on AdS spaces.Comment: 40 pages, 7 figures, uses JHEP. v2: references adde

Shear Viscosity to Entropy Density Ratio in Six Derivative Gravity

We calculate shear viscosity to entropy density ratio in presence of four derivative (with coefficient $\alpha'$) and six derivative (with coefficient $\alpha'^2$) terms in bulk action. In general, there can be three possible four derivative terms and ten possible six derivative terms in the Lagrangian. Among them two four derivative and eight six derivative terms are ambiguous, i.e., these terms can be removed from the action by suitable field redefinitions. Rest are unambiguous. According to the AdS/CFT correspondence all the unambiguous coefficients (coefficients of unambiguous terms) can be fixed in terms of field theory parameters. Therefore, any measurable quantities of boundary theory, for example shear viscosity to entropy density ratio, when calculated holographically can be expressed in terms of unambiguous coefficients in the bulk theory (or equivalently in terms of boundary parameters). We calculate $\eta/s$ for generic six derivative gravity and find that apparently it depends on few ambiguous coefficients at order $\alpha'^2$. We calculate six derivative corrections to central charges $a$ and $c$ and express $\eta/s$ in terms of these central charges and unambiguous coefficients in the bulk theory.Comment: 29 pages, no figure, V2, results and typos correcte

Holographic Renormalization of Foliation Preserving Gravity and Trace Anomaly

From the holographic renormalizationg group viewpoint, while the scale transformation plays a primary role in the duality by providing the extra dimension, the special conformal transformation seems to only play a secondary role. We, however, claim that the space-time diffeomorphism is crucially related to the latter. For its demonstration, we study the holographic renormalization group flow of a foliation preserving diffeomophic theory of gravity (a.k.a. space-time flipped Horava gravity). We find that the dual field theory, if any, is only scale invariant but not conformal invariant. In particular, we show that the holographic trace anomaly in four-dimension predicts the Ricci scalar squared term that would be incompatible with the Wess-Zumino consistency condition if it were conformal. This illustrates how the foliation preserving diffeomophic theory of gravity could be inconsistent with a theorem of the dual unitary quantum field theory.Comment: 18 pages, v2: reference added, v3: comments on more recent literature added in response to referee's reques

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