Antisymmetric relation

About: Antisymmetric relation is a research topic. Over the lifetime, 3322 publications have been published within this topic receiving 64365 citations. The topic is also known as: antisymmetric property & anti-symmetric property.

Matter in transition

Abstract: We explore a novel type of transition in certain 6D and 4D quantum field theories, in which the matter content of the theory changes while the gauge group and other parts of the spectrum remain invariant. Such transitions can occur, for example, for SU(6) and SU(7) gauge groups, where matter fields in a three-index antisymmetric representation and the fundamental representation are exchanged in the transition for matter in the two-index antisymmetric representation. These matter transitions are realized by passing through superconformal theories at the transition point. We explore these transitions in dual F-theory and heterotic descriptions, where a number of novel features arise. For example, in the heterotic description the relevant 6D SU(7) theories are described by bundles on K3 surfaces where the geometry of the K3 is constrained in addition to the bundle structure. On the F-theory side, non-standard representations such as the three-index antisymmetric representation of SU(N) require Weierstrass models that cannot be realized from the standard SU(N) Tate form. We also briefly describe some other situations, with groups such as Sp(3), SO(12), and SU(3), where analogous matter transitions can occur between different representations. For SU(3), in particular, we find a matter transition between adjoint matter and matter in the symmetric representation, giving an explicit Weierstrass model for the F-theory description of the symmetric representation that complements another recent analogous construction.

Classical Yang-Baxter equation from supergravity

Abstract: We promote the open-closed string map, originally formulated by Seiberg Witten, to a solution generating prescription in generalized supergravity. The approach hinges on a knowledge of an antisymmetric bivector $\mathrm{\ensuremath{\Theta}}$, built from antisymmetric products of Killing vectors, which is specified by the equations of motion. In the cases we study, the equations of motion reproduce the classical Yang-Baxter equation (CYBE) and $\mathrm{\ensuremath{\Theta}}$ is the most general $r$-matrix solution. Our work generalizes Yang-Baxter deformations to non-coset spaces and unlocks gravity as a means to classify $r$-matrix solutions to the CYBE.

Cortical interactions in texture processing: scale and dynamics.

Abstract: We investigate the neural computations underlying pattern processing with stimuli based on textures balanced for spatial frequency content (and second-order correlations) but not for higher-order correlations (Julesz et al. 1978). Interchange between two such isodipole textures produces a robust human visual evoked potential (VEP). The difference in population activity driven by two isodipole textures is quantified by the antisymmetric component of the VEP. Statistical properties of the textures eliminate contributions from linear mechanisms to the antisymmetric VEP. The dependence of the antisymmetric VEP on check size and fourth-order correlation statistics is used to test nonlinear models for the underlying neural computations. Linear summation, followed by a simple nonlinearity (such as rectification, saturation, or threshold), is inconsistent with the data. More elaborate models, in which a second nonlinear stage combines the output of local nonlinear mechanisms, are consistent with the data, provided that an appropriate spatial scale is chosen for the second stage of processing. For checks 4 min or smaller, the deduced interaction length is 10-15 min. For checks larger than 4 min, the interaction length is proportional to check size.

Phases of chiral gauge theories

Abstract: We discuss the behavior of two non-supersymmetric chiral SU(N) gauge theories, involving fermions in the symmetric and antisymmetric two-index tensor representations respectively. In addition to global anomaly matching, we employ a recently proposed inequality constraint on the number of effective low energy (massless) degrees of freedom of a theory, based on the thermodynamic free energy. Several possible zero temperature phases are consistent with the constraints. A simple picture for the phase structure emerges if these theories choose the phase, consistent with global anomaly matching, that minimizes the massless degree of freedom count defined through the free energy. This idea suggests that confinement with the preservation of the global symmetries through the formation of massless composite fermions is in general not preferred. While our discussion is restricted mainly to bilinear condensate formation, higher dimensional condensates are considered for one case. We conclude by commenting briefly on two related supersymmetric chiral theories. (c) 2000 The American Physical Society.