arXiv subjects

Pradipta S. Pathak

Publications and source records attributed to Pradipta S. Pathak.

4 recordsLinked to original sources

arXiv2026

Holography, Brick Wall and a Little Hierarchy Problem

We propose a heuristic for the brick wall in AdS/CFT: the location where a boundary mode's local bulk energy reaches a (Planckian) UV cut-off. This accomplishes two things: (a) the brick wall is framed as a breakdown criterion for bulk effective field theory, and (b) the definition is boundary-anchored rather than horizon-anchored, aligning it with holography. Near the horizon, spacetime effectively gets cut-off due to blueshift relative to the boundary, and leads to normal modes. By directly computing these new modes for the BTZ black hole, we show that they are qualitatively unchanged from conventional 't Hooftian brick wall normal modes in the relevant part of the spectrum -- successfully reproducing black hole thermodynamics and exterior smooth-horizon correlators, under similar approximations. However, unlike 't Hooft's (and our own previous) calculations, we also do an $exact$ numerical evaluation of the normal mode partition function. This allows us to identify a "little hierarchy" problem in the brick wall paradigm, irrespective of whether it is horizon-anchored or boundary-anchored: because the modes are not exactly degenerate in the $J$-direction, the coefficient of the area law is slightly subleading, unless the brick wall is slightly trans-Planckian. One way to evade the problem is to increase the number of active species. While this is certainly a possibility in string theory, we argue that a natural resolution is to take into account the degrees of freedom intrinsic to the (stretched) horizon, as suggested by the recent results in arXiv:2601.18775. We argue that this will lead to a dominant contribution from a quantum number associated to the radial direction, while retaining the successes of the $J$-degenerate toy model. We discuss the possible significance of these observations for (a) quantum chaos in black holes, and (b) the fuzzball program.

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arXiv2026

Holography with an Inner Boundary: A Smooth Horizon as a Sum over Horizonless States

The (holomorphic) partition function of the Euclidean BTZ black hole with boundary modulus $\tau$, is the $S$-image of the Virasoro vacuum character, $\chi_{\rm vac}(-1/\tau)$. This object decomposes into primaries via the modular $S$-kernel: $\chi_{\rm vac}\left(-\frac{1}{\tau}\right)=\int_{0}^{\infty} dP S_{0P}(P,c)\chi_P(\tau)$. In this paper, we provide a bulk understanding of this spectral resolution using the Chern-Simons formulation of AdS$_3$ gravity with $two$ boundaries: an asymptotic torus and an excised Wilson line at the origin ("stretched horizon"). At infinity, we impose standard AdS$_3$ Drinfel'd-Sokolov (DS) gauge to obtain the Alekseev-Shatashvili (AS) boundary action for a coadjoint orbit. At the inner boundary, removing the Wilson line prepares the state at the cut as a sum over orbits of the $spatial$ cycle. Re-inserting a spatial holonomy Wilson line acts as a delta-function projector onto the corresponding primary, which together with boundary gravitons, reproduces the Virasoro character (e.g., of a conical defect). But we can also consider projectors onto the $conjugate$ basis $\tilde P$, of the dual cycle. A key observation is that this leads to $S$-kernels instead of delta functions, with the BTZ character arising when the dual cycle label is in the exceptional orbit. Our two-boundary construction provides a bulk understanding of BTZ entropy: holonomy zero modes at the horizon have an effective central charge $c_{\rm prim}=c-1$ from the kernel measure (primaries), while the universal Dedekind-$\eta$ in $\chi_P(\tau)$ contributes $c_{\rm desc}=1$ from boundary gravitons (descendants). Together, they reproduce the full Cardy entropy. While our methods are specific to AdS$_3$/CFT$_2$, they are an explicit illustration that smoothness of the (Euclidean) horizon may emerge from a $sum$ over bulk states which are manifestly unsmooth.

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arXiv2024

Holomorphic Factorization at the Quantum Horizon

We identify a horizon-skimming limit under which wave equations around large classes of black holes allow a determination of their low-lying (quasi-)degenerate normal modes. Building on our recent work, we use these ``quantum horizon" normal modes to study the thermodynamics of the parent black holes. A key observation is that the UV inputs (the location of the UV regulator, the number of species, and the cut-off in the angular Casimir quantum number) can all be combined into the freedom in a single real parameter. Remarkably, this parameter has an interpretation as the central charge of a holomorphically factorized 2D CFT, and choosing it to be the Kerr-CFT value reproduces the black hole's detailed thermodynamics from the statistical mechanics of normal modes. This perspective provides a heuristic understanding for why the Kerr-CFT central charge is related to the angular momentum of the black hole. The black holes we consider include Kerr-Newman in 3+1 dimensions and Cvetic-Youm in 4+1 dimensions (with all six charges), and they need not be BPS or extremal. Our results show that a refined version of the 't Hooftian quantum gas can be made fully consistent with the thermodynamics of very general black holes. This ``mechanical" approach to the central charge is not directly reliant on asymptotic symmetries in the extremal limit, where the black hole is often unstable.

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arXiv2023

Normal Modes of the Stretched Horizon: A Bulk Mechanism for Black Hole Microstate Level Spacing

In 1984, 't Hooft famously used a brickwall (aka stretched horizon) to compute black hole entropy up to a numerical pre-factor. This calculation is sometimes interpreted as due to the entanglement of the modes across the horizon, but more operationally, it is simply an indirect count of the semi-classical modes trapped between the stretched horizon and the angular momentum barrier. Because the calculation was indirect, it needed both the mass and the temperature of the black hole as inputs, to reproduce the area. A more conventional statistical mechanics calculation should be able to get the entropy, once the ensemble is specified (say via the energy, in a microcanonical setting). In this paper, we explicitly compute black hole normal modes in various examples, numerically as well as (in various regimes) analytically. The explicit knowledge of normal modes allows us to reproduce $both$ the Hawking temperature as well as the entropy, once the charges are specified, making this a conventional statistical mechanics calculation. A quasi-degeneracy in the angular quantum numbers is directly responsible for the area scaling of the entropy, and is the key distinction between the Planckian black body calculation (volume scaling) and the 't Hooftian calculation (area scaling). We discuss the (rotating) BTZ case in detail and match the thermodynamic quantities $exactly$. Schwarzschild and Kerr normal modes are discussed in less detail using near-horizon approximations. Our calculations reveal a new hierarchy in the angular quantum numbers, which we speculate is related to string theory.

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