Supergravity Side Research Articles

S-wave absorption of scalars by noncommutative D3-branes

On the supergravity side, we study the propagation of the RR scalar and the dilaton in the D3-branes with NS $B$-field. To obtain the noncommutative effect, we consider the case of $B\to \infty(\theta \to\pi/2)$. We approximate this as the smeared D1-brane background with $F_5=H=0$. In this background, the RR scalar induces an instability of the near-horizon geometry. However, it turns out that the RR scalar is nonpropagating, while the dilaton is a physically propagating mode. We calculate the s-wave absorption cross section of the dilaton. One finds $\sigma_0^\phi |_{B\to\infty} \sim (\tilde \omega \tilde R_{\pi \over 2})^{8.9} / \omega^5$ in the leading-order while $\sigma_0^\phi|_{B=0} \sim (\tilde \omega R_0)^{8}/\omega^5$ in the D3-branes without $B$-field. This means that although the dilaton belongs to a minimally coupled scalar in the absence of $B$-field, it becomes a sort of fixed scalar in the limit of $B \to \infty$.

Towards a SDLCQ test of the Maldacena conjecture

We consider the Maldacena conjecture applied to the near horizon geometry of a D1-brane in the supergravity approximation and present numerical results of a test of the conjecture against the boundary field theory calculation using DLCQ. We previously calculated the two-point function of the stress-energy tensor on the supergravity side; the methods of Gubser, Klebanov, Polyakov, and Witten were used. On the field theory side, we derived an explicit expression for the two-point function in terms of data that may be extracted from the supersymmetric discrete light cone quantization (SDLCQ) calculation at a given harmonic resolution. This yielded a well defined numerical algorithm for computing the two-point function. For the supersymmetric Yang-Mills theory with 16 supercharges that arises in the Maldacena conjecture, the algorithm is perfectly well defined; however, the size of the numerical computation prevented us from obtaining a numerical check of the conjecture. We now present numerical results with approximately 1000 times as many states as we previously considered. These results support the Maldacena conjecture and are within 10–15% of the predicted numerical results in some regions. Our results are still not sufficient to demonstrate convergence, and, therefore, cannot be considered to a numerical proof of the conjecture. We present a method for using a “flavor” symmetry to greatly reduce the size of the basis and discuss a numerical method that we use which is particularly well suited for this type of matrix element calculation.

Domain walls of D=5 supergravity and fixed points of N=1 super-Yang–Mills

Employing the AdS/CFT correspondence, we give an explicit supergravity picture for the renormalization group flow of couplings 4-d super-Yang–Mills with four supercharges. The solution represents a domain wall of 5-d, N=2 supergravity, that interpolates between two (different) AdS 5 vacua and is obtained by gauging a U(1) subgroup of the SU(2) R-symmetry. On the supergravity side the domain wall couples only to scalar fields from vector multiplets, but not to scalars from hypermultiplets. We discuss the c-theorem, the β-functions and consider two examples: one is the sugra solution related to Z k orbifolds (corresponding to N=2 SYM) and the other is an orientifold construction for an elliptically fibered CY with F 1 basis (corresponding to N=1 SYM).

Formula omitted] SCFT and M theory on AdS4× Q1,1,1

Coincident M2 branes at a conical singularity are related to M theory on AdS 4× X 7 for an appropriate 7 dimensional Sasaki-Einstein manifold X 7. For X 7= Q 1,1,1=( SU(2)× SU(2)× SU(2))/( U(1)× U(1)) which was found sometime ago, the infrared limit of the theory on N M2 branes was constructed recently. It is the SU( N)× SU( N)× SU( N) gauge theories with three series of chiral fields A i , i=1,2 transforming in the (N, N,1) representation, B j , j=1,2 transforming in the (1,N, N) representation and C k , k=1,2 transforming in the ( N,1,N) representation. From the scalar Laplacian of X 7 on the supergravity side, we discuss the spectrum of chiral primary operators of dual N=2 superconformal field theory in 3 dimensions. We study M5 branes wrapped over 5-cycle of X 7 which were identified as (three types of) baryon like operators made out of N chiral fields recently. We consider M5 brane wrapped over 3-cycle of X 7 which plays the role of domain wall in AdS 4. The new aspect arises when baryon like operators (M5 branes wrapped over 5-cycle) cross a domain wall (M5 brane wrapped over 3-cycle), M2 brane between them must be created.

Dilaton - fixed scalar correlators and AdS5 × S5 - SYM correspondence

We address the question of AdS/CFT correspondence in the case of the 3-point function ⟨O4O4O8⟩. O4 andO8 are particular primary states represented by tr F2 + ... and tr F4 + ... operators in = 4 SYM theory and dilaton ϕ and massive ``fixed'' scalar ν in D = 5 supergravity. While the value of ⟨O4O4O8⟩ computed in large N weakly coupled SYM theory is non-vanishing, the D = 5 action of type IIB supergravity compactified on S5 does not contain ϕϕν coupling and thus the corresponding correlator seems to vanish on theAdS5 side. This is in obvious contradiction with various arguments suggesting non-renormalization of 2- and 3-point functions of states from short multiplets and implying agreement between the supergravity and SYM expressions for them. We propose a natural resolution of this paradox which emphasizes the 10-dimensional nature of the correspondence. The basic idea is to treat the constant mode of the dilaton as a part of the full S5 Kaluza-Klein family of dilaton modes. This leads to a non-zero result for the ⟨O4O4O8⟩ correlator on the supergravity side.

Can DLCQ test the Maldacena conjecture?

We consider the Maldacena conjecture applied to the near horizon geometry of a D1-brane in the supergravity approximation and consider the possibility of testing the conjecture against the boundary field theory calculation using DLCQ. We propose the two point function of the stress energy tensor as a convenient quantity that may be computed on both sides of the correspondence. On the supergravity side, we may invoke the methods of Gubser, Klebanov, Polyakov, and Witten. On the field theory side, we derive an explicit expression for the two point function in terms of data that may be extracted from a DLCQ calculation at a given harmonic resolution. This gives rise to a well defined numerical algorithm for computing the two point function, which we test in the context of free fermions and the 't Hooft model. For the supersymmetric Yang-Mills theory with 16 supercharges that arises in the Maldacena conjecture, the algorithm is perfectly well defined, although the size of the numerical computation grows too fast to admit any detailed analysis at present, and our results are only preliminary. We are, however, able to present more detailed results on the supersymmetric DLCQ computation of the stress energy tensor correlators for two dimensional Yang Mills theories with (1,1) and (2,2) supersymmetries.

Non-perturbative membrane spin-orbit couplings in

Membrane source-probe dynamics is investigated in the framework of the finite N-sector DLCQ M-theory compactified on a transverse two-torus for an arbitrary size of the longitudinal dimension. The non-perturbative two-fermion terms in the effective action of the matrix theory, the (2 + 1)-dimensional supetsymmetric Yang-Mills theory, that are related to the four derivative F 4 terms by the supersymmetry transformation are obtained, including the one-loop term and full instanton corrections. On the supergravity side, we compute the classical probe action up to two-fermion terms based on the classical supermembrane formulation in an arbitrary curved background geometry produced by source membranes satisfying the BPS condition; two-fermion terms correspond to the spin-orbit couplings for membranes. We find precise agreement between the two approaches when the background space-time is chosen to be that of the DLCQ M-theory, which is asymptotically locally anti-de Sitter.

On stringy thresholds in SYM/AdS thermodynamics

We consider aspects of the role of stringy scales and Hagedorn temperatures in the correspondence between various field theories and AdS-type spaces. The boundary theory is set on a toroidal world-volume to enable small scales to appear in the supergravity backgrounds also for low field-theory temperatures. We find that thermodynamical considerations tend to favour background manifolds with no string-size characteristic scales. The gravitational dynamics censors the reliable exposure of Hagedorn physics on the supergravity side, and the system does not allow the study of the Hagedorn scale by low-temperature field theories. These results are obtained following some heuristic assumptions on the character of stringy modifications to the gravitational backgrounds. A rich phenomenology appears on the supergravity side, with different string backgrounds dominating in different regions, which should have field-theoretic consequences. Six-dimensional world-volumes turn out to be borderline cases from several points of view. For lower-dimensional world-volumes, a fully holographic behaviour is exhibited to order 1/ N 2, and open strings in their presence are found to have a thermodynamic Hagedorn behaviour similar to that of closed strings in flat space.

Generalized conformal symmetry in D-brane matrix models

We study in detail the extension of the generalized conformal symmetry proposed previously for D-particles to the case of supersymmetric Yang-Mills matrix models of Dp-branes for arbitrary p. It is demonstrated that such a symmetry indeed exists both in the Yang-Mills theory and in the corresponding supergravity backgrounds produced by Dp-branes. On the Yang-Mills side, we derive the field-dependent special conformal transformations for the collective coordinates of Dp-branes in the one-loop approximation, and show that they coincide with the transformations on the supergravity side. These transformations are powerful in restricting the forms of the effective actions of probe D-branes in the fixed backgrounds of source D-branes. Furthermore, our formalism enables us to extend the concept of (generalized) conformal symmetry to arbitrary configurations of D-branes, which can still be used to restrict the dynamics of D-branes. For such general configurations, however, it cannot be endowed a simple classical space-time interpretation at least in the static gauge adopted in the present formulation of D-branes.

R-current correlators in N = 4 super-Yang-Mills theory from anti-de Sitter supergravity

We test the conjectured relationship between N = 4 super-Yang-Mills theory in four dimensions and IIB supergravity compactified on AdS 5 × S 5 by computing the two- and three-point functions of R-symmetry currents. We observe that the integral expressions describing the general three-point correlator on the supergravity side have a structure similar to one-loop triangle diagrams in N = 4 super-Yang-Mills theory. This allows us to compare the expressions on both sides of the AdS/CFT correspondence without the technical complications of the loop integrations. We confirm that the two- and three-point correspondence arises at only one-loop in the N = 4 super-Yang-Mills theory. Higher-point functions as well as further three-point functions may be analyzed similarly.

Conformal anomaly for dilaton coupled theories from AdS/CFT correspondence

Trace anomaly for dilaton coupled conformal theories on curved background with non-zero dilaton is found from supergravity side as an IR effect using AdS/CFT correspondence. For d=2 it coincides with the conformal anomaly for dilaton coupled scalar (up to total derivative term which is known to be ambiguous). In four-dimensional case we get conformal anomaly for N=4 super YM theory interacting with conformal supergravity. In the same way the calculation of dilaton dependent conformal anomaly in higher dimensions seems to be much easier than using standard QFT methods.

Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity

We study some aspects of Maldacena's large $N$ correspondence between N=4 superconformal gauge theory on D3-brane and maximal supergravity on AdS_5xS_5 by introducing macroscopic strings as heavy (anti)-quark probes. The macroscopic strings are semi-infinite Type IIB strings ending on D3-brane world-volume. We first study deformation and fluctuation of D3-brane when a macroscopic BPS string is attached. We find that both dynamics and boundary conditions agree with those for macroscopic string in anti-de Sitter supergravity. As by-product we clarify how Polchinski's Dirichlet / Neumann open string boundary conditions arise dynamically. We then study non-BPS macroscopic string anti-string pair configuration as physical realization of heavy quark Wilson loop. We obtain quark-antiquark static potential from the supergravity side and find that the potential exhibits nonanalyticity of square-root branch cut in `t Hooft coupling parameter. We put forward the nonanalyticity as prediction for large-N gauge theory at strong `t Hooft coupling limit. By turning on Ramond-Ramond zero-form potential, we also study theta-vacuum angle dependence of the static potential. We finally discuss possible dynamical realization of heavy N-prong string junction and of large-N loop equation via local electric field and string recoil thereof. Throughout comparisons of the AdS-CFT correspondence, we find crucial role played by `geometric duality' between UV and IR scales on directions perpendicular to D3-brane and parallel ones, explaining how AdS5 spacetime geometry emerges out of four-dimensional gauge theory at strong coupling.