Defect loops in gauged Wess-Zumino-Witten models

We consider loop observables in gauged Wess-Zumino-Witten models, and study the action of renormalization group flows on them. In the WZW model based on a compact Lie group G, we analyze at the classical level how the space of renormalizable defects is reduced upon the imposition of global and affine symmetries. We identify families of loop observables which are invariant with respect to an affine symmetry corresponding to a subgroup H of G, and show that they descend to gauge-invariant defects in the gauged model based on G/H. We study the flows acting on these families perturbatively, and quantize the fixed points of the flows exactly. From their action on boundary states, we present a derivation of the "generalized Affleck-Ludwig rule, which describes a large class of boundary renormalization group flows in rational conformal field theories.Comment: 43 pages, 2 figures. v2: a few typos corrected, version to be published in JHE

Three Principles for Quantum Gravity

We postulate that the fundamental principles of Quantum Gravity are diffeomorphism symmetry, unitarity, and locality. Local observables are compatible with diffeomorphism symmetry in the presence of diff anomalies, which modify the symmetry algebra upon quantization. We describe the generalization of the Virasoro extension to the diffeomorphism algebra in several dimensions, and its off-shell representations. These anomalies can not arise in QFT, because the Virasoro-like cocycles are functionals of the observer's spacetime trajectory, which is not present in QFT. Possible implications for physics are discussed.Comment: Added referenc

Topological protection, disorder, and interactions: Survival at the surface of 3D topological superconductors

We consider the interplay of disorder and interactions upon the gapless surface states of 3D topological superconductors. The combination of topology and superconducting order inverts the action of time-reversal symmetry, so that extrinsic time-reversal invariant surface perturbations appear only as "pseudomagnetic" fields (abelian and non-abelian vector potentials, which couple to spin and valley currents). The main effect of disorder is to induce multifractal scaling in surface state wavefunctions. These critically delocalized, yet strongly inhomogeneous states renormalize interaction matrix elements relative to the clean system. We compute the enhancement or suppression of interaction scaling dimensions due to the disorder exactly, using conformal field theory. We determine the conditions under which interactions remain irrelevant in the presence of disorder for symmetry classes AIII and DIII. In the limit of large topological winding numbers (many surface valleys), we show that the effective field theory takes the form of a Finkel'stein non-linear sigma model, augmented by the Wess-Zumino-Novikov-Witten term. The sigma model incorporates interaction effects to all orders, and provides a framework for a controlled perturbative expansion; the inverse spin or thermal conductance is the small parameter. For class DIII we show that interactions are always irrelevant, while in class AIII there is a finite window of stability, controlled by the disorder. Outside of this window we identify new interaction-stabilized fixed points.Comment: 27 pages, 10 figures. v2: published versio

String Theory in the Penrose Limit of AdS_2 x S^2

The string theory in the Penrose limit of AdS_2 x S^2 is investigated. The specific Penrose limit is the background known as the Nappi-Witten spacetime, which is a plane-wave background with an axion field. The string theory on it is given as the Wess-Zumino-Novikov-Witten (WZNW) model on non-semi-simple group H_4. It is found that, in the past literature, an important type of irreducible representations of the corresponding algebra, h_4, were missed. We present this "new" representations, which have the type of continuous series representations. All the three types of representations of the previous literature can be obtained from the "new" representations by setting the momenta in the theory to special values. Then we realized the affine currents of the WZNW model in terms of four bosonic free fields and constructed the spectrum of the theory by acting the negative frequency modes of free fields on the ground level states in the h_4 continuous series representation. The spectrum is shown to be free of ghosts, after the Virasoro constraints are satisfied. In particular we argued that there is no need for constraining one of the longitudinal momenta to have unitarity. The tachyon vertex operator, that correspond to a particular state in the ground level of the string spectrum, is constructed. The operator products of the vertex operator with the currents and the energy-momentum tensor are shown to have the correct forms, with the correct conformal weight of the vertex operator.Comment: 30 pages, Latex, no figure

Idealized computational models for auditory receptive fields

This paper presents a theory by which idealized models of auditory receptive fields can be derived in a principled axiomatic manner, from a set of structural properties to enable invariance of receptive field responses under natural sound transformations and ensure internal consistency between spectro-temporal receptive fields at different temporal and spectral scales. For defining a time-frequency transformation of a purely temporal sound signal, it is shown that the framework allows for a new way of deriving the Gabor and Gammatone filters as well as a novel family of generalized Gammatone filters, with additional degrees of freedom to obtain different trade-offs between the spectral selectivity and the temporal delay of time-causal temporal window functions. When applied to the definition of a second-layer of receptive fields from a spectrogram, it is shown that the framework leads to two canonical families of spectro-temporal receptive fields, in terms of spectro-temporal derivatives of either spectro-temporal Gaussian kernels for non-causal time or the combination of a time-causal generalized Gammatone filter over the temporal domain and a Gaussian filter over the logspectral domain. For each filter family, the spectro-temporal receptive fields can be either separable over the time-frequency domain or be adapted to local glissando transformations that represent variations in logarithmic frequencies over time. Within each domain of either non-causal or time-causal time, these receptive field families are derived by uniqueness from the assumptions. It is demonstrated how the presented framework allows for computation of basic auditory features for audio processing and that it leads to predictions about auditory receptive fields with good qualitative similarity to biological receptive fields measured in the inferior colliculus (ICC) and primary auditory cortex (A1) of mammals.Comment: 55 pages, 22 figures, 3 table