Superconformal Yang-Mills Theory Research Articles

Thermodynamic curvature of the Schwarzschild-AdS black hole and Bose condensation

In the AdS/CFT correspondence, a dynamical cosmological constant Λ in the bulk corresponds to varying the number of colors N in the boundary gauge theory with a chemical potential μ as its thermodynamic conjugate. In this work, within the context of Schwarzschild black holes in AdS5×S5 and its dual finite temperature N=4 superconformal Yang-Mills theory at large N, we investigate thermodynamic geometry through the behavior of the Ruppeiner scalar R. The sign of R is an empirical indicator of the nature of microscopic interactions and is found to be negative for the large black hole branch implying that its thermodynamic characteristics bear qualitative similarities with that of an attraction dominated system, such as an ideal gas of bosons. We find that as the system's fugacity approaches unity, R takes increasingly negative values signifying long range correlations and strong quantum fluctuations signaling the onset of Bose condensation. On the other hand, R for the small black hole branch is negative at low temperatures and positive at high temperatures with a second order critical point which roughly separates the two regions.

On the infrared divergence and global colour in mathcal{N} = 4 Yang-Mills theory

The mathcal{N} = 4 superconformal Yang-Mills theory on flat four-dimensional Minkowski space is a de-confined gauge theory in the sense that the string tension for fundamental representation coloured quarks vanishes. In fact, static fundamental representation quarks which lie in certain half-BPS super-multiplets do not interact at all. An interesting question asks whether such quarks would carry a well-defined global colour charge which, when the gauge is fixed, should have the status of an internal symmetry. We shall present a simple paradigmatic model which suggests that the answer to this question lies in the way in which infrared divergences are dealt with.

A note on NMHV form factors from the Gra\xdfmannian and the twistor string

In this note we investigate Graßmannian formulas for form factors of the chiral part of the stress-tensor multiplet in mathcal{N}=4 superconformal Yang-Mills theory. We present an all-n contour for the G(3, n + 2) Graßmannian integral of NMHV form factors derived from on-shell diagrams and the BCFW recursion relation. In addition, we study other G(3, n + 2) formulas obtained from the connected prescription introduced recently. We find a recursive expression for all n and study its properties. For n ≥ 6, our formula has the same recursive structure as its amplitude counterpart, making its soft behaviour manifest. Finally, we explore the connection between the two Graßmannian formulations, using the global residue theorem, and find that it is much more intricate compared to scattering amplitudes.

Adiabatic regularization for gauge fields and the conformal anomaly

We construct the adiabatic regularization method for a $U(1)$ gauge field in a conformally flat spacetime by quantizing in the canonical formalism the gauge fixed $U(1)$ theory with mass terms for the gauge fields and the ghost fields. We show that the adiabatic expansion for the mode functions and the adiabatic vacuum can be defined in a similar way using WKB-type solutions as the scalar fields. As an application of the adiabatic method, we compute the trace of the energy momentum tensor and reproduces the known result for the conformal anomaly obtained by the other regularization methods. The availability of the adiabatic expansion scheme for gauge field allows one to study the renormalization of the de-Sitter space maximal superconformal Yang-Mills theory using the adiabatic regularization method.

AdS/dS CFT correspondence

We propose and study a holographic dual of the type IIB superstring theory of AdS_5 x S^5 in terms of the N=4 superconformal Yang-Mills theory on dS_4. We use the bulk to boundary formalism to evaluate the boundary correlation functions and verify that it agrees with the expected result in dS conformal field theory. The gauge theory is expected to be UV finite and enjoy exact SL(2,Z) strong-weak duality. As the string theory Green-Schwarz sigma model carries an infinite number of classically conserved charges, it also suggest that the superconformal Yang-Mills theory is integrable and deserves further studies.

A note on the integral equation for the Wilson loop in D = 4 superconformal Yang–Mills theory

We propose an alternative method to study the saddle point equation in the strong coupling limit for the Wilson loop in D = 4 super-Yang–Mills with an SU(N) gauge group and 2N hypermultiplets. This method is based on an approximation of the integral equation kernel which allows us to solve the simplified problem exactly. To determine the accuracy of this approximation, we compare our results with those obtained recently by Passerini and Zarembo. Although less precise, this simpler approach provides an explicit expression for the density of eigenvalues that is used to derive the planar free energy.

On the instantons and the hypermultiplet mass of $ \mathcal{N} = {{2}^{ * }} $ super Yang-Mills on S 4

We show that the physical N=4 super Yang-Mills theory on a four-sphere with an arbitrary gauge group receives no instanton contributions, by clarifying the relation between the hypermultiplet mass and the equivariant parameters of the mass-deformed theory preserving N=2 supersymmetry. The correct relation also implies that N=4 superconformal Yang-Mills theory with gauge group SU(2) corresponds to Liouville theory on a torus with the insertion of a non-trivial operator, rather than the identity as have been claimed in the literature.

Yangian in the twistor string

We study symmetries of the quantized open twistor string. In addition to global PSL(4|4) symmetry, we find non-local conserved currents. The associated non-local charges lead to Ward identities which show that these charges annihilate the string gluon tree amplitudes, and have the same form as symmetries of amplitudes in N=4 super conformal Yang Mills theory. We describe how states of the open twistor string form a realization of the PSL(4|4) Yangian superalgebra.

Exceptional 𝒩 = 6 and 𝒩 = 2AdS4supergravity, and zero-center modules

We study the gauging of the orthosymplectic algebras OSp(6|4) × SO(2) and its ``dual'' OSp(2|4) × SO(6), both based on supergravities with the same exceptional coset SO*(12)/U(6), and gauge group SO(6) × SO(2). The two dual theories are obtained by two different truncations of gauged = 8 AdS4 supergravity. We explicitly study the gauge sector of the two dual theories with the most general group allowed by supersymmetry. The = 6 gravity multiplet has also the exceptional property to be a zero-center module of OSp(6|4), as it is the case for superconformal Yang-Mills theory in four dimensions based on SU(2,2|n) (PSU(2,2|4) for n = 4) or OSp(n|4).

Two-loop test of the 𝒩 = 6 Chern-Simons theoryS-matrix

Starting from the integrable two-loop spin-chain Hamiltonian describing the anomalous dimensions of scalar operators in the planar N=6 superconformal Chern-Simons theory of ABJM, we perform a direct coordinate Bethe ansatz computation of the corresponding two-loop S-matrix. The result matches with the weak-coupling limit of the scalar sector of the all-loop S-matrix which we have recently proposed. In particular, we confirm that the scattering of A and B particles is reflectionless. As a warm up, we first review the analogous computation of the one-loop S-matrix from the one-loop dilatation operator for the scalar sector of planar N=4 superconformal Yang-Mills theory, and compare the result with the all-loop SU(2|2)^{2} S-matrix.

Quantum critical transport, duality, and M theory

We consider charge transport properties of $2+1$ dimensional conformal field theories at nonzero temperature. For theories with only Abelian U(1) charges, we describe the action of particle-vortex duality on the hydrodynamic-to-collisionless crossover function: this leads to powerful functional constraints for self-dual theories. For $\mathcal{N}=8$ supersymmetric, $\mathrm{SU}(N)$ Yang-Mills theory at the conformal fixed point, exact hydrodynamic-to-collisionless crossover functions of the SO(8) R-currents can be obtained in the large $N$ limit by applying the anti-de Sitter/conformal field theory (AdS/CFT) correspondence to M theory. In the gravity theory, fluctuating currents are mapped to fluctuating gauge fields in the background of a black hole in $3+1$ dimensional anti-de Sitter space. The electromagnetic self-duality of the $3+1$ dimensional theory implies that the correlators of the R-currents obey a functional constraint similar to that found from particle-vortex duality in $2+1$ dimensional Abelian theories. Thus the $2+1$ dimensional, superconformal Yang Mills theory obeys a ``holographic self-duality'' in the large $N$ limit, and perhaps more generally.

Black hole as emergent holographic geometry of weakly interacting hot Yang-Mills gas

We demonstrate five-dimensional anti-de Sitter black hole emerges as dual geometry holographic to weakly interacting N=4 superconformal Yang-Mills theory. We first note that an ideal probe of the dual geometry is the Yang-Mills instanton, probing point by point in spacetime. We then study instanton moduli space at finite temperature by adopting Hitchin's proposal that geometry of the moduli space is definable by Fisher-Rao "information geometry". In Yang-Mills theory, the information metric is measured by a novel class of gauge-invariant, nonlocal operators in the instanton sector. We show that the moduli space metric exhibits (1) asymptotically anti-de Sitter, (2) horizon at radial distance set by the Yang-Mills temperature, and (3) after Wick rotation of the moduli space to the Lorentzian signature, a singularity at the origin. We argue that the dual geometry emerges even for rank of gauge groups of order unity and for weak `t Hooft coupling.

BPS operators in Script N = 4 SYM: Calogero models and 2D fermions

A connection between the gauge fixed dynamics of protected operators in superconformal Yang-Mills theory in four dimensions and Calogero systems is established. This connection generalizes the free Fermion description of the chiral primary operators of the gauge theory formed out of a single complex scalar to more general operators. In particular, a detailed analysis of protected operators charged under an su(1|1)contained in psu(2,2|4) is carried out and a class of operators is identified, whose dynamics is described by the rational super-Calogero model. These results are generalized to arbitrary BPS operators charged under an su(2|3) of the superconformal algebra. Analysis of the non-local symmetries of the super-Calogero model is also carried out, and it is shown that symmetry for a large class of protected operators is a contraction of the corresponding Yangian algebra to a loop algebra.

Exact results in planar Script N = 1 superconformal Yang-Mills theory

In the \beta-deformed N=4 supersymmetric SU(N) Yang-Mills theory we study the class of operators O_J = Tr(\Phi_i^J \Phi_k), i\neq k and compute their exact anomalous dimensions for N,J\to\infty. This leads to a prediction for the masses of the corresponding states in the dual string theory sector. We test the exact formula perturbatively up to two loops. The consistency of the perturbative calculation with the exact result indicates that in the planar limit the one--loop condition g^2=h\bar{h} for superconformal invariance is indeed sufficient to insure the {\em exact} superconformal invariance of the theory. We present a direct proof of this point in perturbation theory. The O_J sector of this theory shares many similarities with the BMN sector of the N=4 theory in the large R--charge limit.

Spin models and superconformal Yang–Mills theory

We apply novel techniques in planar superconformal Yang–Mills theory which stress the role of the Yangian algebra. We compute the first two Casimirs of the Yangian, which are identified with the first two local Abelian Hamiltonians with periodic boundary conditions, and show that they annihilate the chiral primary states. We streamline the derivation of the R-matrix in a conventional spin model, and extend this computation to the gauge theory. We comment on higher-loop corrections and higher-loop integrability.

Planar plane-wave matrix theory at the four loop order: Integrability without BMN scaling

We study SU(N) plane-wave matrix theory up to fourth perturbative order in its large N planar limit. The effective Hamiltonian in the closed su(2) subsector of the model is explicitly computed through a specially tailored computer program to perform large scale distributed symbolic algebra and generation of planar graphs. The number of graphs here was in the deep billions. The outcome of our computation establishes the four-loop integrability of the planar plane-wave matrix model. To elucidate the integrable structure we apply the recent technology of the perturbative asymptotic Bethe Ansatz to our model. The resulting S-matrix turns out to be structurally similar but nevertheless distinct to the so far considered long-range spin-chain S-matrices of Inozemtsev, Beisert-Dippel-Staudacher and Arutyunov-Frolov-Staudacher in the AdS/CFT context. In particular our result displays a breakdown of BMN scaling at the four-loop order. That is, while there exists an appropriate identification of the matrix theory mass parameter with the coupling constant of the N=4 superconformal Yang-Mills theory which yields an eigth order lattice derivative for well seperated impurities (naively implying BMN scaling) the detailed impurity contact interactions ruin this scaling property at the four-loop order. Moreover we study the issue of ``wrapping'' interactions, which show up for the first time at this loop-order through a Konishi descendant length four operator.

Spin models and superconformal Yang–Mills theory

Spin models and superconformal Yang–Mills theory

A relation between approaches to integrability in superconformal Yang-Mills theory

We make contact between the infinite-dimensional non-local symmetry of the typeIIB superstring on AdS5xS5 worldsheet theory and a non-abelian infinite-dimensional symmetry algebra for the weakly coupled superconformal gauge theory. We explain why the planar limit of the one-loop dilatation operator is the Hamiltonian of a spin chain, and show that it commutes with the g*2 N = 0 limit of the non-abelian charges.

Systematics of quarter BPS operators in Script N = 4 SYM

A systematic construction is presented of 1/4 BPS operators in N=4 superconformal Yang-Mills theory, using either analytic superspace methods or components. In the construction, the operators of the classical theory annihilated by 4 out of 16 supercharges are arranged into two types. The first type consists of those operators that contain 1/4 BPS operators in the full quantum theory. The second type consists of descendants of operators in long unprotected multiplets which develop anomalous dimensions in the quantum theory. The 1/4 BPS operators of the quantum theory are defined to be orthogonal to all the descendant operators with the same classical quantum numbers. It is shown, to order $g^2$, that these 1/4 BPS operators have protected dimensions.

A relation between approaches to integrability in superconformal Yang-Mills theory

A relation between approaches to integrability in superconformal Yang-Mills theory