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Register a new userThe double-trace spectrum of N=4 SYM at strong coupling
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The spectrum of IIB supergravity on AdS${}_5 times S^5$ contains a number of bound states described by long double-trace multiplets in $mathcal{N}=4$ super Yang-Mills theory at large t Hooft coupling. At large $N$ these states are degenerate and to obtain their anomalous dimensions as expansions in $tfrac{1}{N^2}$ one has to solve a mixing problem. We conjecture a formula for the leading anomalous dimensions of all long double-trace operators which exhibits a large residual degeneracy whose structure we describe. Our formula can be related to conformal Casimir operators which arise in the structure of leading discontinuities of supergravity loop corrections to four-point correlators of half-BPS operators.
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We consider $alpha$ corrections to four-point correlators of half-BPS operators in $mathcal{N}=4$ super Yang-Mills theory in the supergravity limit. By demanding the correct behaviour in the flat space limit, we find that the leading $(alpha)^3$ correction to the Mellin amplitude is fixed for arbitrary charges of the external operators. By considering the mixing of double-trace operators we can find the $(alpha)^3$ corrections to the double-trace spectrum which we give explicitly for $su(4)$-singlet operators. We observe striking patterns in the corrections to the spectra which hint at their common ten-dimensional origin. By extending the observed patterns and imposing them at order $(alpha)^5$ we are able to reproduce the recently found result for the correction to the Mellin amplitude for $langle mathcal{O}_2 mathcal{O}_2 mathcal{O}_p mathcal{O}_p rangle$ correlators. By applying a similar logic to the $[0,1,0]$ channel of $su(4)$ we are able to deduce new results for the correlators of the form $langle mathcal{O}_2 mathcal{O}_3 mathcal{O}_{p-1} mathcal{O}_p rangle$.
We construct the complete spectral curve for an arbitrary local operator, including fermions and covariant derivatives, of one-loop N=4 gauge theory in the thermodynamic limit. This curve perfectly reproduces the Frolov-Tseytlin limit of the full spectral curve of classical strings on AdS_5xS^5 derived in hep-th/0502226. To complete the comparison we introduce stacks, novel bound states of roots of different flavors which arise in the thermodynamic limit of the corresponding Bethe ansatz equations. We furthermore show the equivalence of various types of Bethe equations for the underlying su(2,2|4) superalgebra, in particular of the type Beauty and Beast.
We study the gamma-deformation of the planar N=4 super Yang-Mills theory which breaks all supersymmetries but is expected to preserve integrability of the model. We focus on the operator Tr$(phi_1phi_1)$ built from two scalars, whose integrability description has been questioned before due to contributions from double-trace counterterms. We show that despite these subtle effects, the integrability-based Quantum Spectral Curve (QSC) framework works perfectly for this state and in particular reproduces the known 1-loop prediction. This resolves an earlier controversy concerning this operator and provides further evidence that the gamma-deformed model is an integrable CFT at least in the planar limit. We use the QSC to compute the first 5 weak coupling orders of the anomalous dimension analytically, matching known results in the fishnet limit, and also compute it numerically all the way from weak to strong coupling. We also utilize this data to extract a new coefficient of the beta function of the double-trace operator couplings.
We find a family of complex saddle-points at large N of the matrix model for the superconformal index of SU(N) N=4 super Yang-Mills theory on $S^3 times S^1$ with one chemical potential $tau$. The saddle-point configurations are labelled by points $(m,n)$ on the lattice $Lambda_tau= mathbb{Z} tau +mathbb{Z}$ with $text{gcd}(m,n)=1$. The eigenvalues at a given saddle are uniformly distributed along a string winding $(m,n)$ times along the $(A,B)$ cycles of the torus $mathbb{C}/Lambda_tau$. The action of the matrix model extended to the torus is closely related to the Bloch-Wigner elliptic dilogarithm, and the related Bloch formula allows us to calculate the action at the saddle-points in terms of real-analytic Eisenstein series. The actions of $(0,1)$ and $(1,0)$ agree with that of pure AdS$_5$ and the supersymmetric AdS$_5$ black hole, respectively. The black hole saddle dominates the canonical ensemble when $tau$ is close to the origin, and there are new saddles that dominate when $tau$ approaches rational points. The extension of the action in terms of modular forms leads to a simple treatment of the Cardy-like limit $tauto 0$.
We develop a novel nonperturbative approach to a class of three-point functions in planar $mathcal{N}=4$ SYM based on Thermodynamic Bethe Ansatz (TBA). More specifically, we study three-point functions of a non-BPS single-trace operator and two determinant operators dual to maximal Giant Graviton D-branes in AdS$_5times$S$^{5}$. They correspond to disk one-point functions on the worldsheet and admit a simpler and more powerful integrability description than the standard single-trace three-point functions. We first introduce two new methods to efficiently compute such correlators at weak coupling; one based on large $N$ collective fields, which provides an example of open-closed-open duality discussed by Gopakumar, and the other based on combinatorics. The results so obtained exhibit a simple determinant structure and indicate that the correlator can be interpreted as a generalization of $g$-functions in 2d QFT; an overlap between an integrable boundary state and a state corresponding to the single-trace operator. We then determine the boundary state at finite coupling using the symmetry, the crossing equation and the boundary Yang-Baxter equation. With the resulting boundary state, we derive the ground-state $g$-function based on TBA and conjecture its generalization to other states. This is the first fully nonperturbative proposal for the structure constants of operators of finite length. The results are tested extensively at weak and strong couplings. Finally, we point out that determinant operators can provide better probes of sub-AdS locality than single-trace operators and discuss possible applications.
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