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 <math altimg='si8.svg'><mrow><msubsup><mi>A</mi><mrow><mo>&#8722;</mo><msub><mi>r</mi><mn>1</mn></msub></mrow><msub><mi>s</mi><mn>1</mn></msub></msubsup><msubsup><mi>A</mi><mrow><mo>&#8722;</mo><msub><mi>r</mi><mn>2</mn></msub></mrow><msub><mi>s</mi><mn>2</mn></msub></msubsup></mrow></math> where <math altimg='si9.svg'><msub><mi>A</mi><mrow><mo>&#8722;</mo><mi>n</mi></mrow></msub></math> is a DDF creation operator. Next, we take the infinite &#8220;spin&#8221; limit to arrive at the classical string dynamics. We find a rotating &#8220;floppy&#8221; string lying mostly on a plane which develops a transverse kink.

India

Diptarka Das

Santanu Mandal

Anurag Sarkar

Classical string profile for a class of DDF amplitudes

We find classes of driven conformal field theories (CFT) in d + 1 dimensions with d &gt; 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 β; the β &lt; 1 (β &gt; 1) Hamiltonians can be unitarily related to the standard (Lüscher-Mack) CFT Hamiltonians. The resulting time evolution can be then calculated by performing appropriate conformal transformations. For d ≤ 3 we show that the transformations can be easily obtained in a quaternion formalism. Evolution with such a single Hamiltonian yields qualitatively different time dependences of observables depending on the value of β, with exponential decays characteristic of heating for β &gt; 1, oscillations for β &lt; 1 and power law decays for β = 1. This manifests itself 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 for any β 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.

United States

Sumit Das

Arnab Kundu

Krishnendu Sengupta

Exactly solvable floquet dynamics for conformal field theories in dimensions greater than two

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 the 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 the 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.

Chaotic and thermal aspects in the highly excited string S-matrix

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 <math><msub><mi>t</mi><mn>0</mn></msub></math>. Also, the quartic interaction between the two scalars is turned on at time <math><msub><mi>t</mi><mrow><mi>in</mi></mrow></msub></math>. These break time-translation invariance. In this setup we examine the effects of the relative ordering of <math><msub><mi>t</mi><mn>0</mn></msub></math> and <math><msub><mi>t</mi><mrow><mi>in</mi></mrow></msub></math> on composite operator mixing. We study how such operator mixing affects features of the scalar potential. We find that the late time effective potential can be sensitive enough to the quenches to trigger phase transitions.

Joydeep Chakrabortty

Bidyut Dey

Suraj Prakash

Shakeel Ur Rahaman

Memories of quenches in operator mixing

Recently it has been shown by Almheiri and Lin [1] that the reconstruction of a 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 Sachdev-Ye-Kitaev by deforming the same with “irrelevant” coupling. We find that half-wormholes, as well as the wormholes, persist in the 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) Sachdev-Ye-Kitaev we find nontrivial dynamics of the saddles as the couplings are varied. Curiously, the irrelevant deformations that we consider can also be thought of as an ensemble average over an overall scaling of the original undeformed Hamiltonian with an appropriate probability distribution; this allows for the possibility that half-wormholes may also be present in suitably defined ensemble of theories.

Sridip Pal

Wormholes and half wormholes under irrelevant deformation

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.

Poland

Pawel Caputa

Path integral complexity and Kasner singularities

We study the effectiveness of the numerical bootstrap techniques recently developed in [1] 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 <math><mi>O</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> vector model quantum mechanics, where we find that the bootstrap method yields results which in the large N agree with saddle point analysis.

Jyotirmoy Bhattacharya

Sayan Kumar Das

Ankit Kumar Jha

Moulindu Kundu

Numerical bootstrap in quantum mechanics

We investigate the connection between spacetime wormholes and ensemble averaging in the context of higher spin AdS3/CFT2. Using techniques from modular bootstrap combined with some holographic inputs, we evaluate the partition function of a Euclidean wormhole in AdS3 higher spin gravity. The fixed spin sectors of the dual CFT2 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.

CERN

Shouvik Datta

Higher spin wormholes from modular bootstrap

We study the properties of a conformal field theory (CFT) driven periodically with a continuous protocol characterized by a frequency ω  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 th Renyi entropy (  <math> <msubsup> <mi>S</mi> <mi>n</mi> <mi>m</mi> </msubsup> </math>  $$ {S}_n^m $$ ) 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   <math> <msubsup> <mi>S</mi> <mi>n</mi> <mi>m</mi> </msubsup> </math>  $$ {S}_n^m $$  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.

Roopayan Ghosh

Conformal Floquet dynamics with a continuous drive protocol

We study asymptotics of three point coefficients (light-light-heavy) and two point correlators in heavy states in unitary, compact 2D 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   <math> <mfrac> <mi>c</mi> <mn>32</mn> </mfrac> </math>  $$ \frac{c}{32} $$  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 behaviour of spherical conformal block.