We apply recently developed tools from exceptional field theory to calculate the full Kaluza-Klein spectrum of the AdS$_5$ Pilch-Warner solution of type IIB supergravity. Through the AdS/CFT correspondence this yields detailed information about the spectrum of protected and unprotected operators of the four-dimensional $\mathcal{N}=1$ Leigh-Strassler SCFT, in the planar limit. We also calculate explicitly the superconformal index of the SCFT in this limit and show that it agrees precisely with the spectrum of protected operators in the supergravity calculation.
In here the matrix model approach, by Dijkgraaf and Vafa, is used in order to obtain the effective superpotential for a certain deformation of N=4 SYM discovered by Leigh and Strassler. An exact solution to the matrix model Lagrangian is found and is expressed in terms of elliptic functions.
Using the result of a matrix model computation of the exact glueball superpotential, we investigate the relevant mass perturbations of the Leigh-Strassler marginal ``q'' deformation of N=4 supersymmetric gauge theory. We recall a conjecture for the elliptic superpotential that describes the theory compactified on a circle and identify this superpotential as one of the Hamiltonians of the elliptic Ruijsenaars-Schneider integrable system. In the limit that the Leigh-Strassler deformation is turned off, the integrable system reduces to the elliptic Calogero-Moser system which describes the N=1^* …
We determine the scalar part of the four-loop chiral dilatation operator for Leigh-Strassler deformations of N=4 super Yang-Mills. This is sufficient to find the four-loop anomalous dimensions for operators in closed scalar subsectors. This includes the SU(2) subsector of the (complex) beta-deformation, where we explicitly compute the anomalous dimension for operators with a single impurity. It also includes the "3-string null" operators of the cubic Leigh-Strassler deformation. Our four-loop results show that the rational part of the anomalous dimension is consistent with a conjecture made in…
The success of the identification of the planar dilatation operator of N=4 SYM with an integrable spin chain Hamiltonian has raised the question if this also is valid for a deformed theory. Several deformations of SYM have recently been under investigation in this context. In this work we consider the general Leigh-Strassler deformation. For the generic case the S-matrix techniques cannot be used to prove integrability. Instead we use R-matrix techniques to study integrability. Some new integrable points in the parameter space are found.
We study the large N anomalous dimensions of operators in a Leigh-Strassler deformation of N=4 super Yang-Mills theory. The operators that we study have a bare dimension of order N (so that the large N limit is not captured by planar diagrams) and are AdS/CFT dual to giant gravitons. The diagonalization of the dilatation operator factorizes into two problems. One of these problems is solved using a double coset ansatz. The second problem is equivalent to a set of decoupled harmonic oscillators.
We construct a new class of supersymmetric $AdS_3\times Y_7$ solutions of type IIB supergravity, where $Y_7$ is an $S^5$ fibration over a spindle, which are dual to $d=2$, $\mathcal{N}=(0,2)$ SCFTs. The solutions are constructed in a sub-truncation of $D=5$, $SO(6)$ maximal gauged supergravity and they all lie within the anti-twist class. We show that the central charge computed from the gravity solutions agrees with an anomaly polynomial calculation associated with compactifying the $\mathcal{N}=1$, $d=4$ Leigh-Strassler SCFT on a spindle.
We show that there is a family of two-dimensional $(0,2)$ SCFTs associated with twisted compactifications of the four-dimensional $\mathcal{N}=1$ Leigh-Strassler fixed point on a closed hyperbolic Riemann surface. We calculate the central charges for this class of theories using anomalies and $c$-extremization. In a suitable truncation of the five-dimensional maximal supergravity, we construct supersymmetric $AdS_3$ solutions that are holographic duals of those two-dimensional $(0,2)$ SCFTs. We also exhibit supersymmetric domain wall solutions that are holographically dual to the RG flows betw…
We carry out a perturbative study of the Leigh-Strassler deformed N=4 SYM theory in order to verify that the trihedral Delta(27) symmetry holds in the quantum theory. We show that the Delta(27) symmetry is preserved to two loops (at finite N) by explicitly computing the superpotential. The perturbative superpotential is not holomorphic in the couplings due to finite contributions. However, there exist coupling constant redefinitions that restore holomorphy. Interestingly, the same redefinitions appear (in the work of Jack, Jones and North[hep-ph/9603386]) if one requires the three-loop anomalo…
We consider a full Leigh-Strassler deformation of the ${\cal N}=4$ SYM theory and look for conditions under which the theory would be conformally invariant and finite. Applying the algorithm of perturbative adjustments of the couplings we construct a family of theories which are conformal up to 3 loops in the non-planar case and up to 4 loops in the planar one. We found particular solutions in the planar case when the conformal condition seems to be exhausted in the one loop order. Some of them happen to be unitary equivalent to the real beta-deformed ${\cal N}=4$ SYM theory, while others are …
The Dijkgraaf-Vafa approach is used in order to study the Coulomb branch of the Leigh-Strassler massive deformation of N=4 SYM with gauge group U(N). The theory has N=1 SUSY and an N-dimensional Coulomb branch of vacua, which can be described by a family of ``generalized'' Seiberg-Witten curves. The matrix model analysis is performed by adding a tree level potential that selects particular vacua. The family of curves is found: it consists of order N branched coverings of a base torus, and it is described by multi-valued functions on the latter. The relation between the potential and the vacuum…
We investigate an exactly marginal N=1 supersymmetric deformation of SU(N) N=4 supersymmetric Yang-Mills theory discovered by Leigh and Strassler. We use a matrix model to compute the exact superpotential for a further massive deformation of the U(N) Leigh-Strassler theory. We then show how the exact superpotential and eigenvalue spectrum for the SU(N) theory follows by a process of integrating-in. We find that different vacua are related by an action of the SL(2,Z) modular group on the bare couplings of the theory extending the action of electric-magnetic duality away from the N=4 theory. We …
We look for chiral primaries in the general Leigh-Strassler deformed N=4 super Yang-Mills theory by systematically computing the planar one-loop anomalous dimension for single trace operators up to dimension six. The operators are organised into representations of the trihedral group, Δ(27), which is a symmetry of the Lagrangian. We find an interesting relationship between the U(1)_R-charge of chiral primaries and the representation of Δ(27) to which the operator belongs. Up to scaling dimension Δ_0=6 (and conjecturally to all dimensions) the following holds: The planar one-loop anomalous dime…
We extend the definition of the star product introduced by Lunin and Maldacena to study marginal deformations of N=4 SYM. The essential difference from the latter is that instead of considering U(1)xU(1) non-R-symmetry, with charges in a corresponding diagonal matrix, we consider two Z_3-symmetries followed by an SU(3) transformation, with resulting off-diagonal elements. From this procedure we obtain a more general Leigh-Strassler deformation, including cubic terms with the same index, for specific values of the coupling constants. We argue that the conformal property of N=4 SYM is preserved,…
We discuss supergraphs and their relation to "chiral functions" in N=4 Super Yang-Mills. Based on the magnon dispersion relation and an explicit three-loop result of Sieg's we make an all loop conjecture for the rational contributions of certain classes of supergraphs. We then apply superspace techniques to the "cubic" branch of Leigh-Strassler N=1 superconformal theories. We show that there are order 2^L/L single trace operators of length L which have zero anomalous dimensions to all loop order in the planar limit. We then compute the anomalous dimensions for another class of single trace ope…
In this paper we study the one-loop dilatation operator of the full scalar field sector of Leigh-Strassler deformed N=4 SYM theory. In particular we map it onto a spin chain and find the parameter values for which the Reshetikhin integrability criteria are fulfilled. Some years ago Roiban found an integrable subsector, consisting of two holomorphic scalar fields, corresponding to the XXZ model. He was pondering about the existence of a subsector which would form generalisation of that model to an integrable su_q(3) model. Later Berenstein and Cherkis added one more holomorphic field and showed…
The conformal index counts the number of exactly marginal deformations. In 4d the index is given by the number of chiral primary operators of dimension 3 moded out by the complexified global group, where the quotient is defined as usual by imposing a D-term. Here we show its consistency with the Leigh-Strassler method for weakly coupled theories, and we test it against known examples. In several examples this method discovers extra exactly marginal deformations beyond those of Leigh-Strassler. [This is an unpublished paper dated 3.3.03.]
We study soft SUSY breaking parameters in the Nelson-Strassler type of models: SUSY standard models coupled with SCFTs. In this type of models, soft SUSY breaking parameters including sfermion masses can be suppressed around the decoupling scale of SCFTs. We clarify the condition to derive exponential suppression of sfermion masses within the framework of pure SCFTs. Such behavior is favorable for degeneracy of sfermion masses. However, the realistic sfermion masses are not quite degenerate due to the gauge couplings and the gaugino masses in the SM sector. We show the sfermion mass spectrum o…
We establish the existence of a quasi-Hopf algebraic structure underlying the Leigh-Strassler N=1 superconformal marginal deformations of the N=4 Super-Yang-Mills theory. The scalar-sector R-matrix of these theories, which is related to their one-loop spin chain Hamiltonian, does not generically satisfy the Quantum Yang-Baxter Equation. By constructing a Drinfeld twist which relates this R-matrix to that of the N=4 SYM theory, but also produces a non-trivial co-associator, we show that the generic Leigh-Strassler R-matrix satisfies the quasi-Hopf version of the QYBE. We also use the twist to d…
Recently it was conjectured that parallel branes at conical singularities are related to string/M theory on $AdS \times X$ where $X$ is an Einstein manifold. In this paper we consider coincident M2 branes near a conifold singularity when M theory is compactified on $AdS_4 \times Q^{1,1,1}$ where $Q^{1,1,1} = (SU(2) \times SU(2) \times SU(2))/(U(1) \times U(1))$ is a seven dimensional Sasaki-Einstein manifold. We argue that M theory on $AdS_4 \times Q^{1,1,1}$ can be described in terms of a three dimensional superconformal field theory.We use the fact that the three dimensional self-mirror dual…
The Leigh-Strassler family of N=1 marginal deformations of the N=4 SYM theory admits a Hopf algebra symmetry which is a quantum group deformation of the SU(3) part of the R-symmetry of the Ncal=4 theory. We investigate how this quantum symmetry might be expressed on the gravity side of the AdS/CFT correspondence. First, we discuss the twist leading to the Hopf algebra structure for the well-known beta-deformation as well as a unitarily equivalent theory that we call the w-deformation. We then show how this Hopf twist can be used to define a star product between the three scalar superfields of …
We construct a continuous one parameter family of $AdS_4\times S^1\times S^5$ S-fold solutions of type IIB string theory which have nontrivial $SL(2,\mathbb{Z})$ monodromy in the $S^1$ direction. The solutions span a subset of a conformal manifold that contains the known $\mathcal{N}=4$ S-fold SCFT in $d=3$, and generically preserve $\mathcal{N}=2$ supersymmetry. We also construct RG flows across dimensions, from $AdS_5\times S^5$, dual to $\mathcal{N}=4$, $d=4$ SYM compactified with a twisted spatial circle, to various $AdS_4\times S^1\times S^5$ S-fold solutions, dual to $d=3$ SCFTs. We cons…
We study a class of near-BPS operators for a complex 2-parameter family of N=1 superconformal Yang-Mills theories that can be obtained by a Leigh-Strassler deformation of N=4 SYM theory. We identify these operators in the large N and large R-charge limit and compute their exact scaling dimensions using N=1 superspace methods. From these scaling dimensions we attempt to reverse-engineer the light-cone worldsheet theory that describes string propagation on the Penrose limit of the dual geometry.
