An official website of the United States government
A bstract The ODE/IM correspondence is an exact link between classical and quantum integrable models. The primary purpose of this work is to show that it remains valid after $$ \textrm{T}\overline{\textrm{T}} $$ T T ¯ perturbation on both sides of the correspondence. In particular, we prove that the deformed Lax pair of the sinh-Gordon model, obtained from the unperturbed one through a dynamical change of coordinates, leads to the same Burgers-type equation governing the quantum spectral flow induced by $$ \textrm{T}\overline{\textrm{T}} $$ T T ¯ . Our main conclusions have general validity, as the analysis may be easily adapted to all the known ODE/IM examples involving integrable quantum field theories.
more »
« less
Quantization of the zigzag model
A bstract The zigzag model is a relativistic integrable N -body system describing the leading high-energy semiclassical dynamics on the worldsheet of long confining strings in massive adjoint two-dimensional QCD. We discuss quantization of this model. We demonstrate that to achieve a consistent quantization of the model it is necessary to account for the non-trivial geometry of phase space. The resulting Poincaré invariant integrable quantum theory is a close cousin of $$ T\overline{T} $$ T T ¯ deformed models.
more »
« less
- Award ID(s):
- 1915219
- PAR ID:
- 10438132
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2022
- Issue:
- 8
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
A bstract We analyze the Thermodynamic Bethe Ansatz (TBA) for various integrable S-matrices in the context of generalized T $$ \overline{\mathrm{T}} $$ T ¯ deformations. We focus on the sinh-Gordon model and its elliptic deformation in both its fermionic and bosonic realizations. We confirm that the determining factor for a turning point in the TBA, interpreted as a finite Hagedorn temperature, is the difference between the number of bound states and resonances in the theory. Implementing the numerical pseudo-arclength continuation method, we are able to follow the solutions to the TBA equations past the turning point all the way to the ultraviolet regime. We find that for any number k of resonances the pair of complex conjugate solutions below the turning point is such that the effective central charge is minimized. As k → ∞ the UV effective central charge goes to zero as in the elliptic sinh-Gordon model. Finally we uncover a new family of UV complete integrable theories defined by the bosonic counterparts of the S -matrices describing the Φ 1 , 3 integrable deformation of non-unitary minimal models $$ \mathcal{M} $$ M 2 , 2 n +3 .more » « less
-
The quantization of pure 3D gravity with Dirichlet boundaryconditions on a finite boundary is of interest both as a model ofquantum gravity in which one can compute quantities which are ``morelocal" than S-matrices or asymptotic boundary correlators, and forits proposed holographic duality to T\overline{T} T T ¯ -deformedCFTs. In this work we apply covariant phase space methods to deduce thePoisson bracket algebra of boundary observables. The result is aone-parameter nonlinear deformation of the usual Virasoro algebra ofasymptotically AdS _3 3 gravity. This algebra should be obeyed by the stress tensor in any T\overline{T} T T ¯ -deformedholographic CFT. We next initiate quantization of this system within thegeneral framework of coadjoint orbits, obtaining — in perturbationtheory — a deformed version of the Alekseev-Shatashvili symplectic formand its associated geometric action. The resulting energy spectrum isconsistent with the expected spectrum of T\overline{T} T T ¯ -deformedtheories, although we only carry out the explicit comparison to \mathcal{O}(1/\sqrt{c}) 𝒪 ( 1 / c ) in the 1/c 1 / c expansion.more » « less
-
Shor's factoring algorithm, believed to provide an exponential speedup over classical computation, relies on finding the period of an exactly periodic quantum modular multiplication operator. This exact periodicity is the hallmark of an integrable system, which is paradoxical from the viewpoint of quantum chaos, given that the classical limit of the modular multiplication operator is a highly chaotic system that occupies the “maximally random” Bernoulli level of the classical ergodic hierarchy. In this work, we approach this apparent paradox from a quantum dynamical systems viewpoint, and consider whether signatures of ergodicity and chaos may indeed be encoded in such an “integrable” quantization of a chaotic system. We show that Shor's modular multiplication operator, in specific cases, can be written as a superposition of quantized -baker's maps exhibiting more typical signatures of quantum chaos and ergodicity. This work suggests that the integrability of Shor's modular multiplication operator may stem from the interference of other “chaotic” quantizations of the same family of maps, and paves the way for deeper studies on the interplay of integrability, ergodicity, and chaos in and via quantum algorithms. Published by the American Physical Society2024more » « less
-
A<sc>bstract</sc> As has been known since the 90s, there is an integrable structure underlying two-dimensional gravity theories. Recently, two-dimensional gravity theories have regained an enormous amount of attention, but now in relation with quantum chaos — superficially nothing like integrability. In this paper, we return to the roots and exploit the integrable structure underlying dilaton gravity theories to study a late time, largeeSBHdouble scaled limit of the spectral form factor. In this limit, a novel cancellation due to the integrable structure ensures that at each genusgthe spectral form factor grows likeT2g+1, and that the sum over genera converges, realising a perturbative approach to the late-time plateau. Along the way, we clarify various aspects of this integrable structure. In particular, we explain the central role played by ribbon graphs, we discuss intersection theory, and we explain what the relations with dilaton gravity and matrix models are from a more modern holographic perspective.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/JHEP08(2022)047
