Prithvi Narayan

Bio: Prithvi Narayan is an academic researcher from Tata Institute of Fundamental Research. The author has contributed to research in topics: AdS/CFT correspondence & Black brane. The author has an hindex of 21, co-authored 35 publications receiving 1618 citations. Previous affiliations of Prithvi Narayan include Indian Institutes of Technology & Weizmann Institute of Science.

SYK-like Tensor Models on the Lattice

Abstract: We study large $N$ tensor models on the lattice without disorder. We introduce techniques which can be applied to a wide class of models, and illustrate it by studying some specific rank-3 tensor models. In particular, we study Klebanov-Tarnopolsky model on lattice, Gurau-Witten model (by treating it as a tensor model on four sites) and also a new model which interpolates between these two models. In each model, we evaluate various four point functions at large $N$ and strong coupling, and discuss their spectrum and long time behaviors. We find similarities as well as differences from SYK model. We also generalize our analysis to rank-$D$ tensor models where we obtain analogous results as $D=3$ case for the four point functions which we computed. For $D>5$, we are able to compute the next-to-subleading ${1 \over N}$ corrections for a specific four point function.

Chaos in Three-dimensional Higher Spin Gravity

Abstract: We discuss $SL(N,\mathbb{C})$ Chern-Simons higher spin gauge theories in Euclidean AdS$_3$. With appropriate boundary term, we derive the higher spin generalization of Schwarzian on-shell action. We investigate gravitationally dressed bi-locals, and we study the soft higher spin mode expansion to obtain soft mode eigenfunctions. We also derive the spin-$s$ eigenfunction from $\mathcal{W}$-Ward identity and a recursion relation. Using the on-shell action, we evaluate the contributions of the soft higher spin modes to the out-of-time-order correlators, and the corresponding Lyapunov exponent of $SL(N)$ higher spin gravity is found to be ${2\pi \over \beta}(N-1)$.

Chiral 2D "Strange Metals" from N = 4 SYM

Abstract: Familiar field theories may contain closed subsectors made out of only fermions, which can be used to explore new and unusual phases of matter in lower dimensions. We focus on the fermionic su(1,1) sector in N=4 SYM and on its ground states, which are Fermi surface states/operators. By computing their spectrum to order $(g_{YM}^2 N)^2$, we argue that fluctuations around this fermi surface, within the sector and in the limit $k_F\rightarrow\infty$, are governed by a chiral 1+1 dimensional sector of the "strange metal" coset $SU(N)_N \otimes SU(N)_N/SU(N)_{2N}$. On the gravity side, the conjectured dual configuration is an $S=0$ degeneration of a rotating black hole. On general grounds we expect that the near horizon excitations of $(S=0,\Omega=1,J\rightarrow\infty)$ degenerations of black holes will be governed by a chiral sector of a 1+1 CFT.

Quantum groups, non-commutative $AdS_2$, and chords in the double-scaled SYK model

Abstract: We study the double-scaling limit of SYK (DS-SYK) model and elucidate the underlying quantum group symmetry. The DS-SYK model is characterized by a parameter q, and in the q → 1 and low-energy limit it goes over to the familiar Schwarzian theory. We relate the chord and transfer-matrix picture to the motion of a “boundary particle” on the Euclidean Poincaré disk, which underlies the singlesided Schwarzian model. AdS2 carries an action of sl(2,R) ' su(1, 1), and we argue that the symmetry of the full DS-SYK model is a certain q-deformation of the latter, namely U√q(su(1, 1)). We do this by obtaining the effective Hamiltonian of the DSSYK as a (reduction of) particle moving on a lattice deformation of AdS2, which has this U√q(su(1, 1)) algebra as its symmetry. We also exhibit the connection to noncommutative geometry of q-homogeneous spaces, by obtaining the effective Hamiltonian of the DS-SYK as a (reduction of) particle moving on a non-commutative deformation of AdS3. There are families of possibly distinct q-deformed AdS2 spaces, and we point out which are relevant for the DS-SYK model. ar X iv :2 21 2. 13 66 8v 1 [ he pth ] 2 8 D ec 2 02 2

Exactly Solvable 1D Quantum Models with Gamma Matrices

Abstract: In this paper, we write exactly solvable generalizations of 1-dimensional quantum XY and Ising-like models by using 2d-dimensional Gamma (Γ) matrices as the degrees of freedom on each site. We show that these models result in quadratic Fermionic Hamiltonians with Jordan-Wigner like transformations. We illustrate the techniques using a specific case of 4-dimensional Γ matrices and explore the quantum phase transitions present in the model.

Rigid Supersymmetric Theories in Curved Superspace

Abstract: We present a uniform treatment of rigid supersymmetric field theories in a curved spacetime \( \mathcal{M} \), focusing on four-dimensional theories with four supercharges. Our discussion is significantly simpler than earlier treatments, because we use classical background values of the auxiliary fields in the supergravity multiplet. We demonstrate our procedure using several examples. For \( \mathcal{M} = Ad{S_4} \) we reproduce the known results in the literature. A supersymmetric Lagrangian for \( \mathcal{M} = {\mathbb{S}^4} \) exists, but unless the field theory is conformal, it is not reflection positive. We derive the Lagrangian for \( \mathcal{M} = {\mathbb{S}^3} \times \mathbb{R} \) and note that the time direction \( \mathbb{R} \) can be rotated to Euclidean signature and be compactified to \( {\mathbb{S}^1} \) only when the theory has a continuous R-symmetry. The partition function on \( \mathcal{M} = {\mathbb{S}^3} \times {\mathbb{S}^1} \) is independent of the parameters of the flat space theory and depends holomorphically on some complex background gauge fields. We also consider R-invariant \( \mathcal{N} = 2 \) theories on \( {\mathbb{S}^3} \) and clarify a few points about them.

Black Holes and Random Matrices

Abstract: We argue that the late time behavior of horizon fluctuations in large anti-de Sitter (AdS) black holes is governed by the random matrix dynamics characteristic of quantum chaotic systems. Our main tool is the Sachdev-Ye-Kitaev (SYK) model, which we use as a simple model of a black hole. We use an analytically continued partition function |Z(β + it)|2 as well as correlation functions as diagnostics. Using numerical techniques we establish random matrix behavior at late times. We determine the early time behavior exactly in a double scaling limit, giving us a plausible estimate for the crossover time to random matrix behavior. We use these ideas to formulate a conjecture about general large AdS black holes, like those dual to 4D super-Yang-Mills theory, giving a provisional estimate of the crossover time. We make some preliminary comments about challenges to understanding the late time dynamics from a bulk point of view.

Hidden Fermi surfaces in compressible states of gauge-gravity duality

Abstract: General scaling arguments, and the behavior of the thermal entropy density, are shown to lead to an infrared metric holographically representing a compressible state with hidden Fermi surfaces. This metric is characterized by a general dynamic critical exponent, z, and a specic hyperscaling violation exponent, . The same metric exhibits a logarithmic violation of the area law of entanglement entropy, as shown recently by Ogawa et al. (arXiv:1111.1023). We study the dependence of the entanglement entropy on the shape of the entangling region(s), on the total charge density, on temperature, and on the presence of additional visible Fermi surfaces of gauge-neutral fermions; for the latter computations, we realize the needed metric in an Einstein-Maxwell-dilaton theory. All our results support the proposal that the holographic theory describes a metallic state with hidden Fermi surfaces of fermions carrying gauge charges of deconned gauge elds.