| 1. |
- Cavaglia, Andrea, et al.
(författare)
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Exploring the Quantum Spectral Curve for AdS3/CFT2
- 2023
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer. - 1126-6708 .- 1029-8479.
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Tidskriftsartikel (refereegranskat)abstract
- Despite the rich and fruitful history of the integrability approach to string theory on the AdS3×S3×T4 background, it has not been possible to extract many concrete predictions from integrability, except in a strict asymptotic regime of large quantum numbers, due to the severity of wrapping effects. The situation changed radically with two independent and identical proposals for the Quantum Spectral Curve (QSC) for this system in a background of pure Ramond-Ramond flux. This formulation is expected to capture all wrapping effects exactly and describe the full planar spectrum. Massless modes conjecturally manifest themselves in a new property of this QSC: the non-quadratic nature of the branch-cut singularities of the QSC Q-functions. This feature implies new technical challenges in solving the QSC equations as compared to the well-studied case of N=4 SYM. In this paper we resolve these difficulties and obtain the first ever predictions for generic unprotected string excitations. We explain how to extract a systematic expansion around the analogue of the weak 't Hooft coupling limit in N=4 SYM and also obtain high-precision numerical results. This concrete data and others obtainable from the QSC could help to identify the so-far mysterious dual CFT.
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| 2. |
- Ekhammar, Simon
(författare)
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An Exploration of Q-Systems : From Spin Chains to Low-Dimensional AdS/CFT
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The discovery of integrability in the planar limit of the AdS5/CFT4 correspondence has led to impressive progress in the study of string theory and four-dimensional N=4 Super-Yang-Mills. In particular, with the formulation of the Quantum Spectral Curve (QSC) the spectral problem is now solved. The QSC has demonstrated its versatility and usefulness in various other applications, including the study of Wilson lines, conformal bootstrap, and the calculation of structure constants.It would be highly desirable to extend the QSC from AdS5/CFT4 to other instances of the AdS/CFT correspondence, a program so far only fully completed for AdS4/CFT3. Achieving this objective requires a solid understanding of the foundation of the QSC, a so-called analytic Q-system. In this thesis and the included papers, we investigate Q-systems and their algebraic and analytic properties. Inspired by the ODE/IM correspondence we propose Q-systems that encode the conserved charges of integrable models with a simply-laced symmetry algebra. In particular, for the case of D(r) a powerful parameterization of the Q-system using pure spinors is employed to efficiently solve compact rational spin chains and find T-functions solving Hirota equations. The extension from D(r) to the non-simply laced algebra B(2)/C(2) is explained and detailed. While many features are similar the relation between the symmetry of the Q-system and that of the integrable model becomes more intricate. By introducing a new method dubbed Monodromy Bootstrap we construct new Quantum Spectral Curves based on gl(2|2). In particular, one curve is conjectured to describe planar string theory on AdS3 with pure RR-flux. We solve the curve in a weak coupling limit both analytically and numerically.We also discuss the problem of finding the eigenvalue spectrum of operators on the squashed seven-sphere coming from the compactification of eleven-dimensional supergravity. These eigenvalues are of importance for the mass spectrum of fields in AdS4.
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| 3. |
- Ekhammar, Simon, et al.
(författare)
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Bethe Algebra using Pure Spinors
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We propose a gl(r)-covariant parameterisation of Bethe algebra appearing in so(2r) integrable models, demonstrate its geometric origin from a fused flag, and use it to compute the spectrum of periodic rational spin chains, for various choices of the rank r and Drinfeld polynomials.
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| 4. |
- Ekhammar, Simon, et al.
(författare)
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Extended systems of Baxter Q-functions and fused flags I: simply-laced case
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- The spectrum of integrable models is often encoded in terms of commuting functions of a spectral parameter that satisfy functional relations. We propose to describe this commutative algebra in a covariant way by means of the extended Q-system that comprise Q-vectors in each of the fundamental representations of the (Langlands dual of) the underlying symmetry algebra. These Q-vectors turn out to parameterise a collection of complete flags which are fused with one another in a particular way. We show that the fused flag is a finite-difference oper in a particular gauge, explicit identification depends on a choice of a Coxeter element. The paper considers the case of simple Lie algebras with a simply-laced Dynkin diagram. For the Ar series, the construction coincides with already known results in the literature. We apply the proposed formalism to the case of the Dr series and the exceptional algebras Er, r=6,7,8. In particular, we solve Hirota bilinear equations in terms of Q-functions and give the explicit character solution of the extended Q-system in the Dr case. We also show how to build up the extended Q-system of Dr type starting either from vectors, by a procedure similar to the Ar scenario which however constructs a fused flag of isotropic spaces, or from pure spinors, via fused Fierz relations.Finally, for the case of rational, trigonometric, and elliptic spin chains, we propose an explicit ansatz for the analytic structure of Q-functions of the extended Q-system. We conjecture that the extended Q-system constrained in such a way is always in bijection with the Bethe algebra of commuting transfer matrices of these models and moreover can be used to show that the Bethe algebra has a simple joint spectrum.
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| 5. |
- Ekhammar, Simon, et al.
(författare)
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Monodromy bootstrap for SU(2|2) quantum spectral curves : from Hubbard model to AdS3/CFT2
- 2022
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer Nature. - 1126-6708 .- 1029-8479. ; 2022:3
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Tidskriftsartikel (refereegranskat)abstract
- We propose a procedure to derive quantum spectral curves of AdS/CFT type by requiring that a specially designed analytic continuation around the branch point results in an automorphism of the underlying algebraic structure. In this way we derive four new curves. Two are based on SU(2|2) symmetry, and we show that one of them, under the assumption of square root branch points, describes Hubbard model. Two more are based on SU(2|2) × SU(2|2). In the special subcase of zero central charge, they both reduce to the unique nontrivial curve which furthermore has analytic properties compatible with PSU(1, 1|2) × PSU(1, 1|2) real form. A natural conjecture follows that this is the quantum spectral curve of AdS/CFT integrable system with AdS3 × S3 × T4 background supported by RR-flux. We support the conjecture by verifying its consistency with the massive sector of asymptotic Bethe equations in the large volume regime. For this spectral curve, it is compulsory that branch points are not of the square root type which qualitatively distinguishes it from the previously known cases.
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| 6. |
- Ekhammar, Simon, et al.
(författare)
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On the squashed seven-sphere operator spectrum
- 2021
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Ingår i: Journal of High Energy Physics. - : Springer Nature. - 1029-8479 .- 1126-6708. ; 2021:12
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Tidskriftsartikel (refereegranskat)abstract
- We derive major parts of the eigenvalue spectrum of the operators on the squashed seven-sphere that appear in the compactification of eleven-dimensional supergravity. These spectra determine the mass spectrum of the fields in AdS4 and are important for the corresponding N = 1 supermultiplet structure. This work is a continuation of the work in [1] where the complete spectrum of irreducible isometry representations of the fields in AdS4 was derived for this compactification. Some comments are also made concerning the G2 holonomy and its implications on the structure of the operator equations on the squashed seven-sphere.
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| 7. |
- Ekhammar, Simon, et al.
(författare)
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The ABJM Hagedorn Temperature from Integrability
- 2023
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Ingår i: Journal of High Energy Physics (JHEP). - : Springer. - 1126-6708 .- 1029-8479. ; :10
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Tidskriftsartikel (refereegranskat)abstract
- We use the quantum spectral curve to compute the Hagedorn temperature for ABJM theory in terms of the interpolating function h(lambda). At weak coupling we compute this temperature up to eight-loop order, showing that it matches the known tree-level and two-loop results. At strong coupling we compute the dependence numerically, showing that it is consistent with expectations from supergravity and the plane-wave limit for the four leading terms in the strong coupling expansion, up to an overall shift of the zero-point energy for type IIA string theory on AdS4 x DOUBLE-STRUCK CAPITAL CP3. We conjecture an analytic form for this shift to leading order that is consistent with our numerical results.
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| 8. |
- Ekhammar, Simon, et al.
(författare)
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The asymptotic form of the Hagedorn temperature in planar N=4 super Yang-Mills
- 2023
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Ingår i: Journal of Physics A. - : Institute of Physics (IOP). - 1751-8113 .- 1751-8121. ; 56:43
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Tidskriftsartikel (refereegranskat)abstract
- Using the supergravity dual and the plane-wave limit as a guide, we conjecture the asymptotic large coupling form of the Hagedorn temperature for planar N=4 super Yang-Mills to order 1/root lambda . This is two orders beyond the presently known behavior. Using the quantum spectral curve procedure of Harmark and Wilhelm, we show that our conjectured form is in excellent agreement with the numerical results.
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