PSU(2,2|4) Character of Quasiclassical AdS/CFT

Nikolay Gromov; Vladimir Kazakov; Zengo Tsuboi

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PSU(2,2|4) Character of Quasiclassical AdS/CFT

Nikolay Gromov, Vladimir Kazakov, Zengo Tsuboi

High Energy Physics - Theory · Submitted 22 Feb 2010

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The authors' main claim We propose a concise first Weyl-type formula for these characters and show that they correctly reproduce the results of quasiclassical one-loop quantization in all sectors of the superstring, under some natural assumptions.

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We solve the recently proposed T- and Y-systems (Hirota equation) for the exact spectrum of AdS/CFT in the strong coupling scaling limit for an arbitrary quasiclassical string state. The corresponding T-functions appear to be super-characters of the SU(2,2|4) group in unitary representations with a highest weight, with the classical AdS5xS5 superstring monodromy matrix as the group element. We propose a concise first Weyl-type formula for these characters and show that they correctly reproduce the results of quasiclassical one-loop quantization in all sectors of the superstring, under some natural assumptions. We also speculate about possible relation between the T-functions and the quantum monodromy matrix.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We solve the recently proposed T- and Y-systems (Hirota equation) for the exact spectrum of AdS/CFT in the strong coupling scaling limit for an arbitrary quasiclassical string state.	contribution 0.86	0.94	0.29	asserted 1.00
s1	The corresponding T-functions appear to be super-characters of the SU(2,2\|4) group in unitary representations with a highest weight, with the classical AdS5xS5 superstring monodromy matrix as the group element.	interpretation 0.52	0.72	0.31	hedged possibility 0.97
s2	We propose a concise first Weyl-type formula for these characters and show that they correctly reproduce the results of quasiclassical one-loop quantization in all sectors of the superstring, under some natural assumptions.	contribution 0.67	0.95	0.61	asserted 0.97
s3	We also speculate about possible relation between the T-functions and the quantum monodromy matrix.	future work 0.97	0.37	0.04	speculative 1.00

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Original abstract

We solve the recently proposed T- and Y-systems (Hirota equation) for the exact spectrum of AdS/CFT in the strong coupling scaling limit for an arbitrary quasiclassical string state. The corresponding T-functions appear to be super-characters of the SU(2,2|4) group in unitary representations with a highest weight, with the classical AdS5xS5 superstring monodromy matrix as the group element. We propose a concise first Weyl-type formula for these characters and show that they correctly reproduce the results of quasiclassical one-loop quantization in all sectors of the superstring, under some natural assumptions. We also speculate about possible relation between the T-functions and the quantum monodromy matrix.

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Cited by 9 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Quantum spectral curve for AdS_5/CFT_4
hep-th 2013-05 conditional novelty 8.0 of 10

A finite nonlinear Riemann-Hilbert system on four Q-functions and a 4x4 matrix replaces the infinite TBA equations for the planar N=4 SYM spectrum.
Quantum spectral curve for arbitrary state/operator in AdS$_5$/CFT$_4$
hep-th 2014-05 accept novelty 7.0 of 10

The authors derive a finite set of Riemann-Hilbert equations (the Quantum Spectral Curve) from the analytic Y-system and recast it as a gl(4|4) Q-system, recovering the asymptotic Bethe ansatz and the classical spectr...
Solving the AdS/CFT Y-system
hep-th 2011-10 conditional novelty 7.0 of 10

The infinite AdS5/CFT4 Y-system is reduced to a finite set of nonlinear integral equations using analyticity and a quantum Z4 symmetry, and checked against Konishi-operator numerics.
TBA, NLO Luscher correction, and double wrapping in twisted AdS/CFT
hep-th 2011-08 accept novelty 7.0 of 10

Two independent finite-volume methods, Lüscher corrections and the thermodynamic Bethe ansatz, agree exactly for the ground-state energy of twisted AdS/CFT, yielding the first double-wrapping correction and a six-loop...
Thermal Giant Graviton Expansion
hep-th 2026-10 accept novelty 6.0 of 10

Exact finite-N and infinite-N expansions of free SYM partition functions are derived from chiral holography, with D-instantons resumming to the Hagedorn temperature.

Show 4 more citing papers

T-system on T-hook: Grassmannian Solution and Twisted Quantum Spectral Curve
hep-th 2015-10 conditional novelty 6.0 of 10

A Grassmannian exterior-form formalism solves the Hirota T-system on T-hooks and yields a twisted Quantum Spectral Curve that reproduces the gamma-twisted BMN vacuum energy at single-wrapping order.
Quantum folded string and integrability: from finite size effects to Konishi dimension
hep-th 2011-02 conditional novelty 6.0 of 10

The Konishi operator's anomalous dimension at strong coupling is derived analytically as 2λ^{1/4} - 4 + 2/λ^{1/4}, confirming earlier numerical Y-system predictions.
Wronskian Solution for AdS/CFT Y-system
hep-th 2010-10 conditional novelty 6.0 of 10

The full quantum Y-system of planar AdS5/CFT4 is solved in closed form as Wronskian determinants of eight Baxter Q-functions, with explicit large-size asymptotic expressions.
T-systems and Y-systems in integrable systems
hep-th 2010-10 accept novelty 3.0 of 10

A unified review shows how T-systems and Y-systems connect solvable lattice models, quantum affine algebras, cluster algebras, dilogarithm identities, and gauge/string applications.

How the literature uses it

38 arXiv papers cite this in 92 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 72 sentences without a confident label

Builds on it 2 papers

This solution will be a natural generalization of our explicit general solution, found by three of the current authors [ref] for a simplified T-system[called in mathematical literature the Q-system, with no explicit spectral parameter dependence (see for examples, [ref] and references therein)], relevant to the quasiclassical limit of the string sigma-model, in terms of characters of specific infinite-dimensional representations of $U(2,2|4)$, parameterized by 8 eigenvalues of an arbitrary group element.

Wronskian Solution for AdS/CFT Y-system · Introduction · 0.93
In this paper, we have continued our trials [ref] (and also [ref] ) to construct T-and Q-functions/operators for integrable models related to quantum affine (super)algebras and establish Wronskian-type formulas for any representations and functional relations among them.

Wronskian solutions of the T, Q and Y-systems related to infinite dimensional unitarizable modules of the general linear superalgebra gl(M|N) · Concluding remarks · 0.85

Uses its method or tool 2 papers

The rest of the $T_a,s(h)$ can be restored by means of the Jacobi-Trudi type formula: [equation] It is easy to see (at least on Mathematica, using the code given in [ref] ) that $T_a,s0$ only for $(a,s)∈𝕋$ where by $𝕋$ we denote the $𝕋$-hook drawn on Fig.[ref](left).

Wronskian Solution for AdS/CFT Y-system · The character solution of the simplified AdS/CFT Y-system in $𝕋$-hook · 0.86
The analysis is significantly harder and not as transparent as the one carried out here, but the comparison may be done order by order in the wrapping parameter $∼e^-L$, using the character solution for the $$-system [ref] .

Structure constants of short operators in planar $\mathcal{N}=4$ SYM theory · Advanced checks · 0.86

Compares with it 4 papers

Its main advantage w.r.t. the previous solutions [ref] of the Y-system (and the associated T-system) in the $𝕋$-hook is its absolutely explicit form in terms of the Wronskian determinants of a finite number of Baxter's Q-functions (7 independent Q-functions) which does not include any infinite sums or integral operators.

Wronskian Solution for AdS/CFT Y-system · Introduction · 1.00
It is interesting to compare these quasi-momenta with the ones for the closed string case presented in [ref] and in [ref] : the (conserved) quantity $𝒬_2$ is present in $p̂_i$ just like in the closed string case, while the $𝒬_1=∑_jx_j/x_j^2-1$ is absent from $p̃_i$.

Spectral curve for open strings attached to the Y=0 brane · States in the $su(2)$ sector · 0.99
In particular for $m_1=m_2=n_1=n_2=2$, [ref] -[ref] reduce to the determinant solution [ref] of the Q-system for AdS/CFT.

Wronskian solutions of the T, Q and Y-systems related to infinite dimensional unitarizable modules of the general linear superalgebra gl(M|N) · Other expressions of the solutions · 0.93

Cites it as support 1 paper

For instance it contains [ref] [ref] the spectrum of the quasi-classical string at large 't Hooft coupling (see e.g. [ref] ).

First-principles derivation of the AdS/CFT Y-systems · Introduction · 0.96

Cites it as background 9 papers

The operator $_R(u)$ is understood [ref] [ref] as the trace of the monodromy matrix associated to the one-parameter family of flat connections of the string worldsheet theory [ref] .

Fusion of line operators in conformal sigma-models on supergroups, and the Hirota equation · Introduction · 0.81
These equations were proposed in [ref] , following the discovery of the Y-system [ref] , and passed a number of important checks [ref] .

Solving the AdS/CFT Y-system · Equivalence of FiNLIE to the TBA equations · 0.97
For the periodic, closed string case the solutions of the AdS/CFT $Y$ and $T$ systems are obtained in the strong coupling scaling limit in [ref] .

Spectral curve for open strings attached to the Y=0 brane · Quasimomenta from the $Y$ system · 0.93

What it cites · 87 sentences without a confident label

Builds on 4 papers

In this paper we construct the complete solution of the AdS/CFT Y-system in the strong coupling limit generalizing [ref] and reproduce from this solution the equations arising for the quasiclassical one-loop corrections of [ref] .

Y-system and Quasi-Classical Strings · Introduction · 1.00
In this paper we construct the complete solution of the AdS/CFT Y-system in the strong coupling limit generalizing [ref] and reproduce from this solution the equations arising for the quasiclassical one-loop corrections of [ref] .

Constructing the AdS/CFT dressing factor · Introduction · 1.00
In our case we have to take $M_1=M_2=2, N=4$ and the generalized partition is represented by a rectangular $a×(s-2)$ Young diagram [equation] On the level of representation, the Q-system for these representations follows from the decomposition of the tensor product of representations in the Theorem 6.1 in [ref] .

Character Formula for Infinite Dimensional Unitarizable Modules of the General Linear Superalgebra · Description of the general construction · 0.88

Uses the method or tool of 1 paper

In particular it was used in [ref] to write the integral equation for excited states.

Integrability for the Full Spectrum of Planar AdS/CFT II · Introduction · 0.81

Compares with 6 papers

Then we use this asymptotic solution of the Y-system to identify our $SU(2,2|4)$ character solution [ref] with the full quasiclassical result of [ref] containing the complete one-loop approximation of the Metsaev-Tseytlin sigma-model around any classical finite gap solution.

Complete 1-loop test of AdS/CFT · Solution of Y-system in the scaling limit and quasiclassical strings · 0.97
[ref] we find that we deal with a class of representations called “unitarizable irreducible $gl(M_1|N|M_2)$-modules”[or $gl_M_1+M_2|0+N$ in the notations of [ref] ].

Rational semistandard tableaux and character formula for the Lie superalgebra $\hat{\frak{gl}}_{\infty|\infty}$ · Description of the general construction · 0.96
[ref] we find that we deal with a class of representations called “unitarizable irreducible $gl(M_1|N|M_2)$-modules”[or $gl_M_1+M_2|0+N$ in the notations of [ref] ].

Character Formula for Infinite Dimensional Unitarizable Modules of the General Linear Superalgebra · Description of the general construction · 0.96

Cites as background 20 papers

Let us remind the asymptotic large $L$ solution of the Y-system [ref] compatible with the ABA of [ref] .

Integrability for the Full Spectrum of Planar AdS/CFT · Asymptotic solution in scaling limit · 0.94
Let us remind the asymptotic large $L$ solution of the Y-system [ref] compatible with the ABA of [ref] .

Transcendentality and Crossing · Asymptotic solution in scaling limit · 0.94
Let us remind the asymptotic large $L$ solution of the Y-system [ref] compatible with the ABA of [ref] .

Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings · Asymptotic solution in scaling limit · 0.94

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