Super-R\'enyi Entropy & Wilson Loops for N=4 SYM and their Gravity Duals

We compute the supersymmetric R\'enyi entropies across a spherical entanglement surface in N=4 SU(N) SYM theory using localization on the four-dimensional ellipsoid. We extract the leading result at large N and \lambda, and match its universal part to a gravity calculation involving a hyperbolically sliced supersymmetric black hole solution of N=4+ SU(2) X U(1) gauged supergravity in five dimensions. We repeat the analysis in the presence of a Wilson loop insertion and find again a perfect match with the dual string theory. Understanding the Wilson loop operator requires knowledge of the full ten-dimensional IIB supergravity solution which we elaborate upon.Comment: 30+1 pages, 1 table; minor corrections, references added; matches published version (JHEP

The Effects of Topical Dose Delivery of Corticosterone on the Development and Hatching Success of the Zebra Finch

The Australian Zebra Finch (Taeniopygia guttata) is an important animal model for vertebrate development and behavior. New research initiatives in the fields of epigenetics rely heavily on injecting hormones and environmental toxins directly into the eggs of different bird species such as zebra finches and other passerine songbirds to replicate the effects maternal condition on offspring. However, the widely used method of egg-injections does not accurately replicate physiological conditions, as the injected substances remain concentrated at the injection site for extended periods and do not diffuse into the developing tissues. Therefore, we propose an alternative method to injection protocols that takes advantage of the porous nature of eggs. Corticosterone (CORT), a major vertebrate stress hormone, dissolved in ethyl alcohol was applied to the surface of zebra finch eggs daily. The effect of this treatment on decreasing hatching success shows that topical hormonal treatments are a viable alternative to egg injection

Constraints on Flavored 2d CFT Partition Functions

We study the implications of modular invariance on 2d CFT partition functions with abelian or non-abelian currents when chemical potentials for the charges are turned on, i.e. when the partition functions are "flavored". We begin with a new proof of the transformation law for the modular transformation of such partition functions. Then we proceed to apply modular bootstrap techniques to constrain the spectrum of charged states in the theory. We improve previous upper bounds on the state with the greatest "mass-to-charge" ratio in such theories, as well as upper bounds on the weight of the lightest charged state and the charge of the weakest charged state in the theory. We apply the extremal functional method to theories that saturate such bounds, and in several cases we find the resulting prediction for the occupation numbers are precisely integers. Because such theories sometimes do not saturate a bound on the full space of states but do saturate a bound in the neutral sector of states, we find that adding flavor allows the extremal functional method to solve for some partition functions that would not be accessible to it otherwise.Comment: 45 pages, 16 Figures v3: typos corrected, expanded appendix on numeric implementatio

Spinning Geodesic Witten Diagrams

We present an expression for the four-point conformal blocks of symmetric traceless operators of arbitrary spin as an integral over a pair of geodesics in Anti-de Sitter space, generalizing the geodesic Witten diagram formalism of Hijano et al [arXiv:1508.00501] to arbitrary spin. As an intermediate step in the derivation, we identify a convenient basis of bulk three-point interaction vertices which give rise to all possible boundary three point structures. We highlight a direct connection between the representation of the conformal block as a geodesic Witten diagram and the shadow operator formalism.Comment: 28+6 pages, 8 figure

The Most Irrational Rational Theories

We propose a two-parameter family of modular invariant partition functions of two-dimensional conformal field theories (CFTs) holographically dual to pure three-dimensional gravity in anti de Sitter space. Our two parameters control the central charge, and the representation of $SL(2,\mathbb{Z})$. At large central charge, the partition function has a gap to the first nontrivial primary state of $\frac{c}{24}$. As the $SL(2,\mathbb{Z})$ representation dimension gets large, the partition function exhibits some of the qualitative features of an irrational CFT. This, for instance, is captured in the behavior of the spectral form factor. As part of these analyses, we find similar behavior in the minimal model spectral form factor as $c$ approaches $1$.Comment: 25 pages plus appendices, 11 figure

Scaling dimensions of monopole operators in the CPNb−1\mathbb{CP}^{N_b - 1} theory in 2+12+1 dimensions

We study monopole operators at the conformal critical point of the $\mathbb{CP}^{N_b - 1}$ theory in $2+1$ spacetime dimensions. Using the state-operator correspondence and a saddle point approximation, we compute the scaling dimensions of these operators to next-to-leading order in $1/N_b$. We find remarkable agreement between our results and numerical studies of quantum antiferromagnets on two-dimensional lattices with SU($N_b$) global symmetry, using the mapping of the monopole operators to valence bond solid order parameters of the lattice antiferromagnet.Comment: 29 pages + Appendices, 3 figures; v2 corrected an important minus sign error and made various improvement