Chethan N Gowdigere | Searcharxiv

arXiv2021

Conformal Bootstrap Signatures of the Tricritical Ising Universality Class

We study the tricritical Ising universality class using conformal bootstrap techniques. By studying bootstrap constraints originating from multiple correlators on the CFT data of multiple OPEs, we are able to determine the scaling dimension of the spin field $Δ_σ$ in various non-integer dimensions $2 \le d \le 3$. $Δ_σ$ is connected to the critical exponent $η$ that governs the (tri-)critical behaviour of the two point function via the relation, $η= 2 - d + 2 Δ_σ$. Our results for $Δ_σ$ match with the exactly known values in two and three dimensions and are a conjecture for non-integer dimensions. We also compare our CFT results for $Δ_σ$ with $ε$-expansion results, available up to $ε^3$ order. Our techniques can be naturally extended to study higher-order multi-critical points.

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arXiv2014

On the smoothness of horizons in the most generic multi center black hole and membrane solutions

We study the differentiability of the metric and other fields at any of the horizons of the \emph{most generic} multi center Reissner-Nordstrom black hole solutions in $d \ge 5$ and of multi center $M2$ brane solutions. Most generic means that the centers are generically located in transverse space and consequently the solutions do not have any transverse spatial isometries. We construct the Gaussian null co-ordinate system for the neighborhood of a horizon by solving (all) the geodesic equations in expansions of (appropriate powers of) the affine parameter. Organizing the harmonic functions that appear in the solution in terms of generalized Gegenbauer polynomials, introduced in \cite{Gowdigere:2014aca}, is key to obtaining the solution to the geodesic equations in a compact and manageable form. We then compute the metric and other fields in the Gaussian null co-ordinate system and find that the differentiability of the horizon in the most generic solution is \emph{identical to} the differentiability of the horizon in the two center/collinear solution (centers distributed on a line in transverse space). We isolate those aspects of the computation that are most relevant to this result. We perform these computations in some cases, in several co-ordinate systems.

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