BFKL spectrum of $$ \mathcal{N} $$ = 4: non-zero conformal spin

146

A simple probe of chaos and operator growth in many-body quantum systems is the out of time ordered four point function. In a large class of local systems, the effects of chaos in this correlator build up exponentially fast inside the so called butterfly cone. It has been previously observed that the growth of these effects is organized along rays and can be characterized by a velocity dependent Lyapunov exponent, λ(v). We show that this exponent is bounded inside the butterfly cone as λ(v) ≤ 2πT (1 − |v|/v B ), where T is the temperature and v B is the butterfly speed. This result generalizes the chaos bound of Maldacena, Shenker and Stanford. We study λ(v) in some examples such as two dimensional SYK models and holographic gauge theories, and observe that in these systems the bound gets saturated at some critical velocity v * < v B . In this sense, boosting a system enhances chaos. We discuss the connection to conformal Regge theory, where λ(v) is related to the spin of the leading large N Regge trajectory, and controls the four point function in an interpolating regime between the Regge and the light cone limit. Finally, we comment on the generalization of the chaos bound to boosted and rotating ensembles and clarify some recent results on this in the literature.

Section: Critical Velocity and Exchange Of Dominancementioning

confidence: 99%

Chaos in the butterfly cone

Mezei

Sárosi

2020

146

“…indices (i, j) ∈ {(1, 2), (2, 1), (3,4), (4, 3)} lead to a finite result for the integral (8.8) when the Q-functions are on-shell i.e. all QSC analyticity constraints are satisfied including the gluing condition [85,86]. For the more general deformed setup of two states with different twists, we expect again that the integrals are convergent for generic pairings the same way as was discussed in section 6.…”

Section: Jhep06(2021)131mentioning

confidence: 99%

Separation of variables in AdS/CFT: functional approach for the fishnet CFT

Cavaglià

Gromov²,

Levkovich-Maslyuk³

2021

Self Cite

The major simplification in a number of quantum integrable systems is the existence of special coordinates in which the eigenstates take a factorised form. Despite many years of studies, the basis realising the separation of variables (SoV) remains unknown in $$ \mathcal{N} $$ N = 4 SYM and similar models, even though it is widely believed they are integrable. In this paper we initiate the SoV approach for observables with nontrivial coupling dependence in a close cousin of $$ \mathcal{N} $$ N = 4 SYM — the fishnet 4D CFT. We develop the functional SoV formalism in this theory, which allows us to compute non-perturbatively some nontrivial observables in a form suitable for numerical evaluation. We present some applications of these methods. In particular, we discuss the possible SoV structure of the one-point correlators in presence of a defect, and write down a SoV-type expression for diagonal OPE coefficients involving an arbitrary state and the Lagrangian density operator. We believe that many of the findings of this paper can be applied in the $$ \mathcal{N} $$ N = 4 SYM case, as we speculate in the last part of the article.

“…The Quantum Spectral Curve (QSC) has become an indispensable tool of precision spectroscopy in AdS 5 /CFT 4 and AdS 4 /CFT 3 holographic models [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. For a review on the QSC, see [21].…”

Section: Introductionmentioning

confidence: 99%

Quantum Spectral Curve for AdS3/CFT2: a proposal

Cavaglià

Gromov

Stefański

et al. 2021

Self Cite

We conjecture the Quantum Spectral Curve equations for string theory on AdS3× S3× T4 with RR charge and its CFT2 dual. We show that in the large-length regime, under additional mild assumptions, the QSC reproduces the Asymptotic Bethe Ansatz equations for the massive sector of the theory, including the exact dressing phases found in the literature. The structure of the QSC shares many similarities with the previously known AdS5 and AdS4 cases, but contains a critical new feature — the branch cuts are no longer quadratic. Nevertheless, we show that much of the QSC analysis can be suitably generalised producing a self-consistent system of equations. While further tests are necessary, particularly outside the massive sector, the simplicity and self-consistency of our construction suggests the completeness of the QSC.