arXiv subjects
Publications and source records attributed to A. Schwimmer.
We apply Srednicki's regularization to extract the logarithmic term in the entanglement entropy produced by tracing out a real, massless, scalar field inside a three dimensional sphere in 3+1 flat spacetime. We find numerically that the coefficient of the logarithm is -1/90 to 0.2 percent accuracy, in agreement with an existing analytical result.
The holographic representation of the entanglement entropy of four dimensional conformal field theories is studied. By generalizing the replica trick the anomalous terms in the entanglement entropy are evaluated. The same terms in the holographic representation are calculated by a method which does not require the solution of the equations of motion or a cut off. The two calculations disagree for rather generic geometries. The reasons for the disagreement are analyzed.
The special properties of scalars having a mass such that the two possible dimensions of the dual scalar respect the unitarity and the Breitenlohner-Freedman bounds and their ratio is integral (``resonant scalars'') are studied in the AdS/CFT correspondence. The role of logarithmic branches in the gravity theory is related to the existence of a trace anomaly and to a marginal deformation in the Conformal Field Theory. The existence of asymptotic charges for the conformal group in the gravity theory is interpreted in terms of the properties of the corresponding CFT.
We present a holographic treatment of Chern-Simons (CS) gravity theories in odd dimensions. We construct the associated holographic stress tensor and calculate the Weyl anomalies of the dual CFT.
We study the mechanism by which gravitational actions reproduce the trace anomalies of the holographically related conformal field theories. Two universal features emerge: a) the ratios of type B trace anomalies in any even dimension are independent of the gravitational action, being uniquely determined by the underlying algebraic structure b) the normalization of the type A and the overall normalization of the type B anomalies are given by action dependent expressions with the dimension dependence completely fixed.
We study D-branes that preserve a diagonal SL(2) affine Lie algebra in string theory on AdS_3. We find three classes of solutions, corresponding to the following representations of SL(2): (1) degenerate, finite dimensional representations with half integer spin, (2) principal continuous series, (3) principal discrete series. We solve the bootstrap equations for the vacuum wave functions and discuss the corresponding open string spectrum. We argue that from the point of view of the AdS/CFT correspondence, the above D-branes introduce boundaries with conformal boundary conditions into the two dimensional spacetime. Open string vertex operators correspond to boundary perturbations. We also comment on the geometric interpretation of the branes.
Using the Weyl transfomations induced by diffeomorphisms we set up a cohomological problem for the Fefferman-Graham coefficients. The cohomologically nontrivial solutions remove the ambiguity and give the nonlocal terms in the effective action responsible for the trace anomalies.
Using the relation between diffeomorphisms in the bulk and Weyl transformations on the boundary we study the Weyl transformation properties of the bulk metric on shell and of the boundary action. We obtain a universal formula for one of the classes of trace anomalies in any even dimension in terms of the parameters of the gravity action.
We present two novel derivations of the recently established $(-)^p$ factor in the charge quantization condition for $p$-brane dyon sources in spacetime dimension $D$=$2p$+2. The first requires consistency of the condition under the charge shifts produced by (generalized) $θ$-terms. The second traces the sign difference between adjoining dimensions to compactification effects.
We discuss some aspects of the relation between space-time properties of branes in string theory, and the gauge theory on their worldvolume, for models invariant under four supercharges in three and four dimensions. We show that a simple set of rules governing brane dynamics reproduces many features of gauge theory. We study theories with $U(N_c)$, $SO(N_c)$ and $Sp(N_c)$ gauge groups and matter in the fundamental and two index tensor representations, and use the brane description to establish Seiberg's electric-magnetic duality for these models.
We study in detail the space of perturbations of a pair of dual $N=1$ supersymmetric theories based on an $SU(N_c)$ gauge theory with an adjoint $X$ and fundamentals with a superpotential which is polynomial in $X$. The equivalence between them depends on non-trivial facts about polynomial equations, i.e.\ singularity theory. The classical chiral rings of the two theories are different. Quantum mechanically there are new relations in the chiral rings which ensure their equivalence. Duality interchanges ``trivial'' classical relations in one theory with quantum relations in the other and vice versa. We also speculate about the behavior of the theory without the superpotential.
We discuss non-abelian $SU(N_c)$ gauge theory coupled to an adjoint chiral superfield $X$, and a number of fundamental chiral superfields $Q^i$. Using duality, we show that turning on a superpotential $W(X)=\Tr\sum_{l=1}^k g_l X^{l+1}$ leads to non-trivial long distance dynamics, a large number of multicritical IR fixed points and vacua, connected to each other by varying the coefficients $g_l$.
We discuss two dimensional Yang -- Mills theories with massless fermions in arbitrary representations of a gauge group $G$. It is shown that the physics (spectrum and interactions) of the massive states in such models is independent of the detailed structure of the model, and only depends on the gauge group $G$ and an integer $k$ measuring the total anomaly. The massless physics, which does depend on the details of the model, decouples (almost) completely from that of the massive one. As an example, we discuss the equivalence of QCD$_2$ coupled to fermions in the adjoint, and fundamental representations.
A class of two-dimensional globally scale-invariant, but not conformally invariant, theories is obtained. These systems are identified in the process of discussing global and local scaling properties of models related by duality transformations, based on non-semisimple isometry groups. The construction of the dual partner of a given model is followed through; non-local as well as local versions of the former are discussed.
The problem of maintaining scale and conformal invariance in Maxwell and general N-form gauge theories away from their critical dimension d=2(N+1) is analyzed.We first exhibit the underlying group-theoretical clash between locality,gauge,Lorentz and conformal invariance require- ments. "Improved" traceless stress tensors are then constructed;each violates one of the above criteria.However,when d=N+2,there is a duality equivalence between N-form models and massless scalars.Here we show that conformal invariance is not lost,by constructing a quasilocal gauge invariant improved stress tensor.The correlators of the scalar theory are then reproduced,including the latter's trace anomaly.
A class of string backgrounds associated with non semi-simple groups is obtained as a special large level limit of ordinary WZW models. The models have an integer Virasoro central charge and they include the background recently studied by Nappi and Witten.
We give a complete geometric description of conformal anomalies in arbitrary, (necessarily even) dimension. They fall into two distinct classes: the first, based on Weyl invariants that vanish at integer dimensions, arises from finite -- and hence scale-free -- contributions to the effective gravitational action through a mechanism analogous to that of the (gauge field) chiral anomaly. Like the latter, it is unique and proportional to a topological term, the Euler density of the dimension, thereby preserving scale invariance. The contributions of the second class, requiring introduction of a scale through regularization, are correlated to all local conformal scalar polynomials involving powers of the Weyl tensor and its derivatives; their number increases rapidly with dimension. Explicit illustrations in dimensions 2, 4 and 6 are provided.
The fusion of fields in a rational conformal field theory gives rise to a ring structure which has a very particular form. All such rings studied so far were shown to arise from some potentials. In this paper the fusion rings of the WZW models based on the symplectic group are studied. It is shown that they indeed arise from potentials which are described. These potentials give rise to new massive perturbations of superconformal hermitian symmetric models. The metric of the perturbation is computed and is shown to be given by solutions of the sinh--gordon equation. The kink structure of the theories is described, and it is argued that these field theories are integrable. The $S$ matrices for the fusion theories are argued to be non--minimal extensions of the $G_k\times G_1/ G_{k+1}$ $S$ matrices with the adjoint perturbation, in the case of $G=SU(N)$.