A. Schwimmer

Remarks on the canonical quantization of the Chern-Simons-Witten theory

Abstract We comment on some aspects of the canonical quantization of the Chern-Simons-Witten theory. We carry out explicitly the quantization on several interesting surfaces. The connection to the related two dimensional theory is illustrated from different points of view.

On renormalization group flows in four dimensions

A bstractWe discuss some general aspects of renormalization group flows in four dimensions. Every such flow can be reinterpreted in terms of a spontaneously broken conformal symmetry. We analyze in detail the consequences of trace anomalies for the effective action of the Nambu-Goldstone boson of broken conformal symmetry. While the c-anomaly is algebraically trivial, the a-anomaly is “non-Abelian”, and leads to a positive-definite universal contribution to the S-matrix element of 2 → 2 dilaton scattering. Unitarity of the S-matrix results in a monotonically decreasing function that interpolates between the Euler anomalies in the ultraviolet and the infrared, thereby establishing the a-theorem.

Comments on the N = 2,3,4 superconformal algebras in two dimensions

Abstract We discuss the extended superconformal algebras (SCAs) in two dimensions. A general classification of the different algebras is presented. It is shown that the Neveu-Schwarz and the Ramond N = 2 SCAs are equivalent. We find two N = 3 SCAs and discuss their representations. Unitary highest weight representations of these algebras in terms of one boson and one fermion ( c = 3 2 are exhibited. We also find an infinite set of N = 4 SCAs and we comment on their representations.

On duality in supersymmetric Yang-Mills theory

Abstract We discuss non-abelian SU(Nc) 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) = TrΣl=1k glXl+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 gl.

Asymptotic dynamics and asymptotic symmetries of three-dimensional extended AdS supergravity

Abstract We investigate systematically the asymptotic dynamics and symmetries of all three-dimensional extended AdS supergravity models. First, starting from the Chern–Simons formulation, we show explicitly that the (super)anti-de Sitter boundary conditions imply that the asymptotic symmetry algebra is the extended superconformal algebra with quadratic nonlinearies in the currents. We then derive the super-Liouville action by solving the Chern–Simons theory and obtain a realization of the superconformal algebras in terms of super-Liouville fields. Finally, we discuss the possible periodic conditions that can be imposed on the generators of the algebra and generalize the spectral flow analysed previously in the context of the N-extended linear superconformal algebras with N⩽4. The (2+1)-AdS/2-CFT correspondence sheds a new light on the properties of the nonlinear superconformal algebras. It also provides a general and natural interpretation of the spectral flow.

Entanglement entropy, trace anomalies and holography☆

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.

Factoring out free fermions and superconformal algebras

Abstract It is shown that any meromorphic conformal field theory can be written as the tensor product of a free (Neveu-Schwartz) fermion conformal field theory and one with no conformal weight 1 2 fields. By applying this to the N =3 and an N =4 superconformal algebra, the structure of their unitary representations is elucidated.

A class of string backgrounds as a semiclassical limit of WZW models

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.Abstract 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 recently studied by Nappi and Witten.

On Scale and Conformal Invariance in Four Dimensions

A bstractWe study the implications of scale invariance in four-dimensional quantum field theories. Imposing unitarity, we find that infinitely many matrix elements vanish in a suitable kinematical configuration. This vanishing is a nontrivial necessary condition for conformality. We provide an argument why this is expected to be a sufficient condition as well, thereby linking scale and conformal invariance in unitary theories. We also discuss possible exceptions to our argument.

The Phase Structure of SU(N)/Z(N) Lattice Gauge Theories

Abstract The phase structure of pure SU( N )/Z( N ) lattice gauge theories in four dimensions is discussed. The presence of Z N monopoles plausibly leads to a phase transition. A Monte Carlo simulation of SO (3) shows the presence of a very strong, may be first order, phase transition.