arXiv subjects

Diptarka Das

Publications and source records attributed to Diptarka Das.

At least 19 recordsLinked to original sources

arXiv2026

Non-relativistic Floquet Conformal Field Theory

We develop a formalism for studying Floquet dynamics for systems with non-relativistic conformal invariance in d spatial dimensions. Our analysis indicates the existence of two dynamical phases, hyperbolic and elliptic, separated by a parabolic transition surface. We demonstrate this by studying the fidelity of the driven state and the expectation value of a conformal generator in the many body ground state during the drive. Stroboscopically, they behave exponentially in the hyperbolic phase, show oscillatory behavior in the elliptic phase, and exhibit power-law on the transition surface. Our analysis is completely universal and can be directly applied to several systems including trapped fermions near unitarity and resonant anyons. The former can provide experimental signatures of these dynamical phases. We also comment on a holographic perspective of such driven non-relativistic CFTs and demonstrate that the hyperbolic phase is associated with a timelike stationary-limit surface, such as an ergosphere, in the bulk, while the parabolic phase corresponds to an extremal Killing horizon.

hep-th↗

arXiv2026

Bootstrapping black holes at low impact parameter

We use the stringy dispersion relation (SDR) to ask the following question about gravitational effective field theories: once the universal large-impact-parameter eikonal carrier is supplied, where does the remaining positive spectrum go? Working in six dimensions for concreteness, we include the complete high-spin continuum tail of the carrier and first work at weak coupling, where $M_{\rm Pl}>M_{\rm EFT}$. The extremal spectra contain a saturated low-impact band whose outer edge stays at roughly five to six times the inverse EFT scale even as the gravitational radius shrinks. The same edge is reproduced by a strict $G_N=0$ capped-SDR problem on the present grids. Thus the weak-coupling band approaches an intrinsic non-gravitational baseline of the capped extremal problem. On a common high-energy grid, a coupling ladder crossing $M_{\rm Pl}=M_{\rm EFT}$ resolves the cap-saturated support as a wedge: its outer envelope has the rotating black-hole homogeneity $G_N^{1/3}E^ {4/3}$, while its approximately linear lower envelope flattens as $G_N$ grows. We then use the deliberately reversed hierarchy $M_{\rm Pl}<M_ {\rm EFT}$ as a microscope for strong-gravity structure. In this regime a cap-saturated low-impact band follows an order-one Giddings-Porto rotating black-hole scale, a separate Regge-like ridge appears at high spin and low energies, the broad available region between these structures and the eikonal layer remains mostly empty, while at the far-tail of energy, series of Regge trajectories emerge.

hep-th↗

arXiv2025

Eigenstate Thermalization in 1+1-Dimensional SU(2) Lattice Gauge Theory Coupled with Dynamical Fermions

We test the eigenstate thermalization hypothesis (ETH) in 1+1-dimensional SU(2) lattice gauge theory (LGT) with one flavor of dynamical fermions. Using the loop-string-hadron framework of the LGT with a bosonic cut-off, we exactly diagonalize the Hamiltonian for finite size systems and calculate matrix elements (MEs) in the eigenbasis for both local and non-local operators. We analyze different indicators to identify the parameter space for quantum chaos at finite lattice sizes and investigate how the ETH behavior emerges in both the diagonal and off-diagonal MEs. Our investigations allow us to study various time scales of thermalization and the emergence of random matrix behavior, and highlight the interplays of the several diagnostics with each other. Furthermore, from the off-diagonal MEs, we extract a smooth function that is closely related to the spectral function for both local and non-local operators. We find numerical evidence of the spectral gap and the memory peak in the non-local operator case. Finally, we investigate aspects of subsystem ETH in the lattice gauge theory and identify certain features in the subsystem reduced density matrix that are unique to gauge theories.

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arXiv2025

Classical string profile for a class of DDF amplitudes

In the critical bosonic string theory, we explicitly evaluate the three point scattering amplitude at tree level, of a photon with two massive higher spins. The massive excitations belong to states of the form $A_{-r_1}^{s_1} A_{-r_2}^{s_2}$ where $A_{-n}$ is a DDF creation operator. Next, we take the infinite ``spin'' limit to arrive at the classical string dynamics. We find a rotating ``floppy'' string lying mostly on a plane which develops a transverse kink.

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arXiv2025

Dynamical Phases of Higher Dimensional Floquet CFTs

This paper investigates the dynamical phases of Floquet Conformal Field Theories (CFTs) in space-time dimensions greater than two. Building upon our previous work [1] which introduced quaternionic representations for studying Floquet dynamics in higher dimensional CFTs, we now explore more general square pulse drive protocols that go beyond a single SU(1,1) subgroup. We demonstrate that, for multi-step drive protocols, the system exhibits distinct dynamical phases characterized by the nature of the eigenvalues of the quaternionic matrix representing time evolution in a single cycle, leading to different stroboscopic responses. Our analysis establishes a fundamental geometric interpretation where these dynamical phases directly correspond to the presence or absence of Killing horizons in the base space of the CFT and in a higher dimensional AdS space on which a putative dual lives. The heating phase is associated with a non-extremal horizon, the critical phase with an extremal horizon which disappears in the non-heating phase. We develop perturbative approaches to compute the Floquet Hamiltonians in different regimes and show, how tuning drive parameters can lead to horizons, providing a geometric framework for understanding heating phenomena in driven conformal systems.

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arXiv2023

Chaotic and Thermal Aspects in the Highly Excited String S-Matrix

We compute tree level scattering amplitudes involving more than one highly excited states and tachyons in bosonic string theory. We use these amplitudes to understand chaotic and thermal aspects of the excited string states lending support to the Susskind-Horowitz-Polchinski correspondence principle. The unaveraged amplitudes exhibit chaos in the resonance distribution as a function of kinematic parameters, which can be described by random matrix theory. Upon coarse-graining these amplitudes are shown to exponentiate, and capture various thermal features, including features of a stringy version of the eigenstate thermalization hypothesis as well as notions of typicality. Further, we compute the effective string form factor corresponding to the highly excited states, and argue for the random walk behaviour of the long strings.

hep-th↗

arXiv2023

Exactly Solvable Floquet Dynamics for Conformal Field Theories in Dimensions Greater than Two

We find classes of driven conformal field theories (CFT) in d + 1 dimensions with d > 1, whose quench and Floquet dynamics can be computed exactly. The setup is suitable for studying periodic drives, consisting of square pulse protocols for which Hamiltonian evolution takes place with different deformations of the original CFT Hamiltonian in successive time intervals. These deformations are realized by specific combinations of conformal generators with a deformation parameter $\beta$; the $\beta < 1$ ($\beta > 1$) Hamiltonians can be unitarily related to the standard (Luscher-Mack) CFT Hamiltonian. The resulting time evolution can be then calculated by conformal transformations. For $d\leq 3$ we show that the transformations can be obtained in a quaternion formalism. Evolution with such a single Hamiltonian yields qualitatively different time dependences of observables depending on the value of $\beta$, ranging from exponential decays characteristic of heating to oscillations and power law decays. This manifests in the behavior of the fidelity, unequal-time correlator, and the energy density at the end of a single cycle of a square pulse protocol with different hamiltonians in successive time intervals. When the Hamiltonians in a cycle involve generators of a single SU(1, 1) subalgebra we calculate the Floquet Hamiltonian. We show that one can get dynamical phase transitions by varying the time period of a cycle, where the system can go from a non-heating phase which is oscillatory as a function of the time period to a heating phase with an exponentially damped behavior. Our methods can be generalized to other discrete and continuous protocols. We also point out that our results are expected to hold for a broader class of QFTs that possesses an SL(2, C) symmetry with fields that transform as quasi-primaries under this. As an example, we briefly comment on celestial CFTs in this context.

hep-th↗

arXiv2023

Spectral Form Factors of Topological Phases

Signatures of dynamical quantum phase transitions and chaos can be found in the time evolution of generalized partition functions such as spectral form factors (SFF) and Loschmidt echoes. While a lot of work has focused on the nature of such systems in a variety of strongly interacting quantum theories, in this work, we study their behavior in short-range entangled topological phases, particularly focusing on the role of symmetry-protected topological zero modes. We show, using both analytical and numerical methods, how the existence of such zero modes in any representative system can mask the SFF with large period (akin to generalized Rabi) oscillations, hiding any behavior arising from the bulk of the spectrum. Moreover, in a quenched disordered system, these zero modes fundamentally change the late-time universal behavior reflecting the chaotic signatures of the zero-energy manifold. Our study uncovers the rich physics underlying the interplay of chaotic signatures and topological characteristics in a quantum system.

cond-mat.str-el↗

arXiv2022

Memories of quenches in operator mixing

We work perturbatively with an interacting quantum field theory comprised of two distinct scalar fields. In this theory, we introduce a sudden quench of the mass of one of the scalars at time $t_0$. Also, the quartic interaction between the two scalars is turned on at time $t_{in}$. These break time-translation invariance. In this setup we examine the effects of the relative ordering of $t_0$ and $t_{in}$ on composite operator mixing. We study how such operator mixing affect features of the scalar potential. We find that the late time effective potential can be sensitive enough to the quenches to trigger phase transitions.

hep-th↗

arXiv2022

(Half) Wormholes under Irrelevant Deformation

Recently it has been shown by Almheiri and Lin [1] that the reconstruction of black-hole interior is sensitive to knowing the exact coupling of the boundary theory even if the coupling is irrelevant. This motivates us to enlarge the set of the one-time and two-time toy models inspired from the SYK by deforming the same with \textit{irrelevant} coupling. We find that both half-wormholes as well as the wormholes persist in presence of the deformation, leading to a similar mechanism for curing the factorization problem. While for the one time case, the deformed partition function and its moments change by an overall factor, which can completely be absorbed into a renormalization of coupling, for the two time (or coupled one time) SYK we find non-trivial dynamics of the saddles as the couplings are varied. Curiously, the \textit{irrelevant} deformations that we consider can also be thought of as an ensemble average over an overall scaling of the original undeformed Hamiltionian with an appropriate probability distribution, this allows for the possibility that half-wormholes may also be present in suitably defined ensemble of theories.

hep-th↗

arXiv2021

Path Integral Complexity and Kasner singularities

We explore properties of path integral complexity in field theories on time dependent backgrounds using its dual description in terms of Hartle-Hawking wavefunctions. In particular, we consider boundary theories with time dependent couplings which are dual to Kasner-AdS metrics in the bulk with a time dependent dilaton. We show that holographic path integral complexity decreases as we approach the singularity, consistent with earlier results from holographic complexity conjectures. Furthermore, we find examples where the complexity becomes universal i.e., independent of the Kasner exponents, but the properties of the path integral tensor networks depend sensitively on this data.

hep-th↗

arXiv2021

Scrambling under quench

We evaluate out of time ordered correlators in certain low dimensional quantum systems at zero temperature, subjected to homogenous quantum quenches. We find that when the Lyapunov exponent exists, it can be identified with the quenched energy. We show that the exponent naturally gets related to the post-quench effective temperature. In the context of sudden quenches the exponent is determined in terms of the quench amplitude while for smooth quenches we observe scalings (both the Kibble-Zurek as well as the fast) of the exponent with the quench rate. The scalings are identical to that of the energy generated during the quench.

hep-th↗

arXiv2021

Numerical Bootstrap in Quantum Mechanics

We study the effectiveness of the numerical bootstrap techniques recently developed in arXiv:2004.10212 for quantum mechanical systems. We find that for a double well potential the bootstrap method correctly captures non-perturbative aspects. Using this technique we then investigate quantum mechanical potentials related by supersymmetry and recover the expected spectra. Finally, we also study the singlet sector of O(N) vector model quantum mechanics, where we find that the bootstrap method yields results which in the large N agree with saddle point analysis.

hep-th↗

arXiv2021

Higher spin wormholes from modular bootstrap

We investigate the connection between spacetime wormholes and ensemble averaging in the context of higher spin AdS$_3$/CFT$_2$. Using techniques from modular bootstrap combined with some holographic inputs, we evaluate the partition function of a Euclidean wormhole in AdS$_3$ higher spin gravity. The fixed spin sectors of the dual CFT$_2$ exhibit features that starkly go beyond conventional random matrix ensembles: power-law ramps in the spectral form factor and potentials with a double-well/crest underlying the level statistics.

hep-th↗

arXiv2021

Conformal Floquet dynamics with a continuous drive protocol

We study the properties {of a conformal field theory} (CFT) driven periodically with a continuous protocol characterized by a frequency $\omega_D$. Such a drive, in contrast to its discrete counterparts (such as square pulses or periodic kicks), does not admit exact analytical solution for the evolution operator $U$. In this work, we develop a Floquet perturbation theory which provides an analytic, albeit perturbative, result for $U$ that matches exact numerics in the large drive amplitude limit. We find that the drive yields the well-known heating (hyperbolic) and non-heating (elliptic) phases separated by transition lines (parabolic phase boundary). Using this and starting from a primary state of the CFT, we compute the return probability ($P_n$), equal ($C_n$) and unequal ($G_n$) time two-point primary correlators, energy density($E_n$), and the $m^{\rm th}$ Renyi entropy ($S_n^m$) after $n$ drive cycles. Our results show that below a crossover stroboscopic time scale $n_c$, $P_n$, $E_n$ and $G_n$ exhibits universal power law behavior as the transition is approached either from the heating or the non-heating phase; this crossover scale diverges at the transition. We also study the emergent spatial structure of $C_n$, $G_n$ and $E_n$ for the continuous protocol and find emergence of spatial divergences of $C_n$ and $G_n$ in both the heating and non-heating phases. We express our results for $S_n^m$ and $C_n$ in terms of conformal blocks and provide analytic expressions for these quantities in several limiting cases. Finally we relate our results to those obtained from exact numerics of a driven lattice model.

hep-th↗

arXiv2020

Universality in asymptotic bounds and its saturation in $2$D CFT

We study asymptotics of three point coefficients (light-light-heavy) and two point correlators in heavy states in unitary, compact $2$D CFTs. We prove an upper and lower bound on such quantities using numerically assisted Tauberian techniques. We obtain an optimal upper bound on the spectrum of operators appearing with fixed spin from the OPE of two identical scalars. While all the CFTs obey this bound, rational CFTs come close to saturating it. This mimics the scenario of bounds on asymptotic density of states and thereby pronounces an universal feature in asymptotics of 2D CFTs. Next, we clarify the role of smearing in interpreting the asymptotic results pertaining to considerations of eigenstate thermalization in 2D CFTs. In the context of light-light-heavy three point coefficients, we find that the order one number in the bound is sensitive to how close the light operators are from the $\frac{c}{32}$ threshold. In context of two point correlator in heavy state, we find the presence of an enigmatic regime which separates the $AdS_3$ thermal physics and the BTZ black hole physics. Furthermore, we present some new numerical results on the behavior of spherical conformal block.

hep-th↗

arXiv2020

Virasoro blocks and quasimodular forms

We analyse Virasoro conformal blocks in the regime of heavy intermediate exchange $(h_p \rightarrow \infty)$. For the 1-point block on the torus and the 4-point block on the sphere, we show that each order in the large-$h_p$ expansion can be written in closed form as polynomials in the Eisenstein series. The appearance of this structure is explained using the fusion kernel and, more markedly, by invoking the modular anomaly equations via the 2d/4d correspondence. We observe that the existence of these constraints allows us to develop a faster algorithm to recursively construct the blocks in this regime. We then apply our results to find corrections to averaged heavy-heavy-light OPE coefficients.

hep-th↗

arXiv2020

Quantum quench, large N, and symmetry restoration

We globally quench the theory of two dimensional massless fermions (many flavours) with quartic interactions by making the quartic coupling a smooth function of time. Working in a derivative expansion we show that the discrete Z2 symmetry in case of the Gross-Neveu model, and the U(1) symmetry in case of the Nambu-Jona-Lasinio model, are restored during the zero-temperature quench. For the Gross-Neveu model we show that this can be understood as an effective thermalization. The time of symmetry restoration shows scaling with the quench rate. We identify this with the Kibble-Zurek scaling in the problem. In a suitable double scaling limit, the symmetry restoration may be understood in terms of Liouville quantum mechanics.

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