ϵ\epsilon-Expansion in the Gross-Neveu CFT

We use the recently developed CFT techniques of Rychkov and Tan to compute anomalous dimensions in the $O(N)$ Gross-Neveu model in $d=2+\epsilon$ dimensions. To do this, we extend the "cowpie contraction" algorithm of arXiv:1506.06616 to theories with fermions. Our results match perfectly with Feynman diagram computations.Comment: v2: a correction in contraction algorithm (main results unchanged), references and an appendix added, discussion less rushe

Chiral Higher Spin Gravity

We construct a candidate for the most general chiral higher spin theory with AdS$_3$ boundary conditions. In the Chern-Simons language, on the left it has the Drinfeld-Sokolov reduced form, but on the right all charges and chemical potentials are turned on. Altogether (for the spin-3 case) these are $19$ functions. Despite this, we show that the resulting metric has the form of the "most general" AdS$_3$ boundary conditions discussed by Grumiller and Riegler. The asymptotic symmetry algebra is a product of a $\mathcal{W}_3$ algebra on the left and an affine $sl(3)_k$ current algebra on the right, as desired. The metric and higher spin fields depend on all the $19$ functions. We compare our work with previous results in the literature.Comment: v2: refs added, minor correction

A Note on D1-D5 Entropy and Geometric Quantization

We quantize the space of 2-charge fuzzballs in IIB supergravity on $K3$. The resulting entropy precisely matches the D1-D5 black hole entropy, including a specific numerical coefficient. A partial match (ie., a smaller coefficient) was found by Rychkov a decade ago using the Lunin-Mathur subclass of solutions - we use a simple observation to generalize his approach to the full moduli space of $K3$ fuzzballs, filling a small gap in the literature.Comment: v2,3: minor corrections to a footnote and acknowledgments, v1 is the JHEP versio

A Neumann Boundary Term for Gravity

The Gibbons-Hawking-York (GHY) boundary term makes the Dirichlet problem for gravity well defined, but no such general term seems to be known for Neumann boundary conditions. In this paper, we view Neumann {\em not} as fixing the normal derivative of the metric ("velocity") at the boundary, but as fixing the functional derivative of the action with respect to the boundary metric ("momentum"). This leads directly to a new boundary term for gravity: the trace of the extrinsic curvature with a specific dimension-dependent coefficient. In three dimensions this boundary term reduces to a "one-half" GHY term noted in the literature previously, and we observe that our action translates precisely to the Chern-Simons action with no extra boundary terms. In four dimensions the boundary term vanishes, giving a natural Neumann interpretation to the standard Einstein-Hilbert action without boundary terms. We argue that in light of AdS/CFT, ours is a natural approach for defining a "microcanonical" path integral for gravity in the spirit of the (pre-AdS/CFT) work of Brown and York.Comment: v3: emphasized that a covariant notion of Neumann boundary condition inevitably leads to our boundary term. v4: more ref

A Grassmann Path From AdS_3 to Flat Space

We show that interpreting the inverse AdS_3 radius 1/l as a Grassmann variable results in a formal map from gravity in AdS_3 to gravity in flat space. The underlying reason for this is the fact that ISO(2,1) is the Inonu-Wigner contraction of SO(2,2). We show how this works for the Chern-Simons actions, demonstrate how the general (Banados) solution in AdS_3 maps to the general flat space solution, and how the Killing vectors, charges and the Virasoro algebra in the Brown-Henneaux case map to the corresponding quantities in the BMS_3 case. Our results straightforwardly generalize to the higher spin case: the recently constructed flat space higher spin theories emerge automatically in this approach from their AdS counterparts. We conclude with a discussion of singularity resolution in the BMS gauge as an application.Comment: 20 pages, 1 figure; v2: many refs added, minor changes, v3: typos fixed, one more ref added, JHEP versio

Aspects of Higher Spin Theories, Conformal Field Theories and Holography

This dissertation consists of three parts. The first part of the thesis is devoted to the study of gravity and higher spin gauge theories in 2+1 dimensions. The first part deals with cosmological solutions of spin-3 gravity and their thermodynamics, flat space limit of AdS$_3$ gravity and higher spins using Grassmann approach and chiral higher spin solutions with the most general AdS$_3$ boundary condition. The second part is devoted to the problem of Neumann boundary condition in Einstein's gravity. We present an explicit boundary term that makes the Neumann variational problem well posed and explore its consequences for holography in various dimensions. In the third part of the dissertation, we use the CFT techniques of Rychkov and Tan to compute anomalous dimensions in the O(N) Gross-Neveu model in $d=2+\epsilon$ dimensions. To do this, we extend the "cow-pie contraction" algorithm of Basu and Krishnan to theories with fermions.Comment: Slightly expanded version of the PhD thesis, defended on 5th September 2017, supervised by Chethan Krishnan, based on arXiv:1308.6741, arXiv:1312.2941, arXiv:1412.5053, arXiv:1510.05287, arXiv:1605.01603, arXiv:1609.06300, arXiv:1703.0176

3D Gravity, Chern-Simons and Higher Spins: A Mini Introduction

These are notes of introductory lectures on (a) elements of 2+1 dimensional gravity, (b) some aspects of its relation to Chern-Simons theory, (c) its generalization to couple higher spins, and (d) cosmic singularity resolution as an application in the context of flat space higher spin theory. A knowledge of the Einstein-Hilbert action, classical non-Abelian gauge theory and some (negotiable amount of) maturity are the only pre-requisites.Comment: 23 pages, Based on talks/lectures by CK at Goteborg, Tehran and Bangkok. v2:acknowledgments and references added, v3:published versio

Synthesis and electrochemical studies of novel ionic liquid based electrolytes

Room temperature ionic liquids (RTILs) have received substantial interest as nonaqueous electrolytes in lithium ion- and metal-air batteries in recent years due to their low volatility, non-flammability, wide liquid range, and thermal stability characteristics. Towards developing a new generation of high specific energy lithium ion batteries, a series of imidazolium and pyrrolidinium based ionic liquids were synthesized and explored as nonaqueous electrolytes in lithium-, lithium ion-, and lithium-air batteries. Pyrrolidinium-TFSI based ionic liquids have wide electrochemical stability (5.7 - 6.2 V vs Li/Li+); however, they show limited thermal stabilities and lithium cell discharge characteristics. TFSI-based ionic liquids are thermally and electrochemically more stable when compared with their BF4-based analogues. A series of fluorinated ionic liquid electrolytes were synthesized and investigated for their use in lithium-air batteries. These ionic liquids have improved the diffusion coefficient and higher solubility of oxygen when compared with currently used nonaqueous electrolytes. Cathode materials, such as LiNi1/3Mn1/3Co1/3O2 and LiFePO4, were chemically delithiated using nitronium tetrafluoroborate (NO2BF4), or disodium peroxydisulfate (Na2S2O8\u3e), to explore their effect on the oxidative degradation of the carbonate based electrolytes. Using fluoroethylene carbonate as the electrolyte additive, electrolyte degradation was monitored by 19F NMR spectroscopy. Formation of the solid electrolyte interface (SEI) on the delithiated cathode materials was probed using surface techniques, such as X-ray photoelectron spectroscopy (XPS) and scanning electron microscopy (SEM) --Abstract, page iii

Higher Spin Cosmology

We construct cosmological solutions of higher spin gravity in 2+1 dimensional de Sitter space. We show that a consistent thermodynamics can be obtained for their horizons by demanding appropriate holonomy conditions. This is equivalent to demanding the integrability of the Euclidean boundary CFT partition function, and reduces to Gibbons-Hawking thermodynamics in the spin-2 case. By using a prescription of Maldacena, we relate the thermodynamics of these solutions to those of higher spin black holes in AdS_3.Comment: 21 pages, v2: many typos fixed, refs added, v3: minor corrections/improvements, Phys. Rev. D version, v4: one more re