Charges of Exceptionally Twisted Branes

The charges of the exceptionally twisted (D4 with triality and E6 with charge conjugation) D-branes of WZW models are determined from the microscopic/CFT point of view. The branes are labeled by twisted representations of the affine algebra, and their charge is determined to be the ground state multiplicity of the twisted representation. It is explicitly shown using Lie theory that the charge groups of these twisted branes are the same as those of the untwisted ones, confirming the macroscopic K-theoretic calculation. A key ingredient in our proof is that, surprisingly, the G2 and F4 Weyl dimensions see the simple currents of A2 and D4, respectively.Comment: 19 pages, 2 figures, LaTex2e, complete proofs of all statements, updated bibliograph

On the Stellar Kinematics and Mass of the Virgo Ultra-Diffuse Galaxy VCC 1287

Here, we present a kinematical analysis of the Virgo cluster ultra-diffuse galaxy (UDG) VCC 1287 based on data taken with the Keck Cosmic Web Imager (KCWI). We confirm VCC 1287's association both with the Virgo cluster and its globular cluster (GC) system, measuring a recessional velocity of $1116 \pm 2\ \mathrm{km\ s^{-1}}$. We measure a stellar velocity dispersion ($19 \pm 6\ \mathrm{km\ s^{-1}}$) and infer both a dynamical mass ($1.11^{+0.81}_{-0.81} \times 10^{9} \ \mathrm{M_{\odot}}$) and mass to light ratio ($13^{+11}_{-11}$) within the half light radius (4.4 kpc). This places VCC 1287 slightly above the well established relation for normal galaxies, with a higher mass to light ratio for its dynamical mass than normal galaxies. We use our dynamical mass, and an estimate of GC system richness, to place VCC 1287 on the GC number -- dynamical mass relation, finding good agreement with a sample of normal galaxies. Based on a total halo mass derived from GC counts, we then infer that VCC 1287 likely resides in a cored or low concentration dark matter halo. Based on the comparison of our measurements to predictions from simulations, we find that strong stellar feedback and/or tidal effects are plausibly the dominant mechanisms in the formation of VCC 1287. Finally, we compare our measurement of the dynamical mass with those for other UDGs. These dynamical mass estimates suggest relatively massive halos and a failed galaxy origin for at least some UDGs.Comment: 13 pages, 10 figures with an additional 5 pages and 5 figures in appendices. Accepted for publication in MNRAS. v2: with small updates from publication formatting and a minor plotting fix for Fig. 1

Nonlinear field-dependence and f-wave interactions in superfluid 3He

We present results of transverse acoustics studies in superfluid ^{3}He-B at fields up to 0.11 T. Using acoustic cavity interferometry, we observe the Acoustic Faraday Effect for a transverse sound wave propagating along the magnetic field, and we measure Faraday rotations of the polarization as large as 1710^{\circ}. We use these results to determine the Zeeman splitting of the Imaginary Squashing mode, an order parameter collective mode with total angular momentum J=2. We show that the pairing interaction in the f-wave channel is attractive at a pressure of P=6 bar. We also report nonlinear field dependence of the Faraday rotation at frequencies substantially above the mode frequency not accounted for in the theory of the transverse acoustic dispersion relation formulated for frequencies near the mode. Consequently, we have identified the region of validity of the theory allowing us to make corrections to the analysis of Faraday rotation experiments performed in earlier work.Comment: 7 pages, 5 figure

Symmetries of the Kac-Peterson Modular Matrices of Affine Algebras

The characters $\chi_\mu$ of nontwisted affine algebras at fixed level define in a natural way a representation $R$ of the modular group $SL_2(Z)$. The matrices in the image $R(SL_2(Z))$ are called the Kac-Peterson modular matrices, and describe the modular behaviour of the characters. In this paper we consider all levels of $(A_{r_1}\oplus\cdots\oplus A_{r_s})^{(1)}$, and for each of these find all permutations of the highest weights which commute with the corresponding Kac-Peterson matrices. This problem is equivalent to the classification of automorphism invariants of conformal field theories, and its solution, especially considering its simplicity, is a major step toward the classification of all Wess-Zumino-Witten conformal field theories.Comment: 16 pp, plain te

Can a Lattice String Have a Vanishing Cosmological Constant?

We prove that a class of one-loop partition functions found by Dienes, giving rise to a vanishing cosmological constant to one-loop, cannot be realized by a consistent lattice string. The construction of non-supersymmetric string with a vanishing cosmological constant therefore remains as elusive as ever. We also discuss a new test that any one-loop partition function for a lattice string must satisfy.Comment: 14 page

Automorphism Modular Invariants of Current Algebras

We consider those two-dimensional rational conformal field theories (RCFTs) whose chiral algebras, when maximally extended, are isomorphic to the current algebra formed from some affine non-twisted Kac--Moody algebra at fixed level. In this case the partition function is specified by an automorphism of the fusion ring and corresponding symmetry of the Kac--Peterson modular matrices. We classify all such partition functions when the underlying finite-dimensional Lie algebra is simple. This gives all possible spectra for this class of RCFTs. While accomplishing this, we also find the primary fields with second smallest quantum dimension.Comment: 32 pages, plain Te