Giant gravitons and the emergence of geometric limits in $ beta$-deformations of calN=4{ cal N}=4calN=4 SYM (original) (raw)
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Journal of High Energy Physics, 2015
We study a one parameter family of supersymmetric marginal deformations of N = 4 SYM with U(1) 3 symmetry, known as β-deformations, to understand their dual AdS × X geometry, where X is a large classical geometry in the g 2 YM N → ∞ limit. We argue that we can determine whether or not X is geometric by studying the spectrum of open strings between giant gravitons states, as represented by operators in the field theory, as we take N → ∞ in certain double scaling limits. We study the conditions under which these open strings can give rise to a large number of states with energy far below the string scale. The number-theoretic properties of β are very important. When exp(iβ) is a root of unity, the space X is an orbifold. When exp(iβ) close to a root of unity in a double scaling limit sense, X corresponds to a finite deformation of the orbifold. Finally, if β is irrational, sporadic light states can be present.
Complex marginal deformations of D3-brane geometries, their Penrose limits and giant gravitons
Nuclear Physics B, 2007
We apply the Lunin-Maldacena construction of gravity duals to β-deformed gauge theories to a class of Type IIB backgrounds with U(1) 3 global symmetry, which include the multicenter D3-brane backgrounds dual to the Coulomb branch of N = 4 super Yang-Mills and the rotating D3-brane backgrounds dual to the theory at finite temperature and chemical potential. After a general discussion, we present the full form of the deformed metrics for three special cases, which can be used for the study of various aspects of the marginally-deformed gauge theories. We also construct the Penrose limits of the solutions dual to the Coulomb branch along a certain set of geodesics and, for the resulting PP-wave metrics, we examine the effect of β-deformations on the giant graviton states. We find that giant gravitons exist only up to a critical value of the σ-deformation parameter, are not degenerate in energy with the point graviton, and remain perturbatively stable. Finally, we probe the σ-deformed multicenter solutions by examining the static heavy-quark potential by means of Wilson loops. We find situations that give rise to complete screening as well as linear confinement, with the latter arising is an intriguing way reminiscent of phase transitions in statistical systems.
Emergent geometry from q -deformations of Script N = 4 super Yang-Mills
Journal of High Energy Physics, 2006
We study BPS states in a marginal deformation of super Yang-Mills on R × S 3 using a quantum mechanical system of q-commuting matrices. We focus mainly on the case where the parameter q is a root of unity, so that the AdS dual of the field theory can be associated to an orbifold of AdS 5 × S 5 . We show that in the large N limit, BPS states are described by density distributions of eigenvalues and we assign to these distributions a geometrical spacetime interpretation. We go beyond BPS configurations by turning on perturbative non-q-commuting excitations. Considering states in an appropriate BMN limit, we use a saddle point approximation to compute the BMN energy to all perturbative orders in the 't Hooft coupling. We also examine some BMN like states that correspond to twisted sector string states in the orbifold and we show that our geometrical interpretation of the system is consistent with the quantum numbers of the corresponding states under the quantum symmetry of the orbifold.
On exactly marginal deformations of n = 4 sym and type iib supergravity on ads(5) x s**5
2013
N = 4 supersymmetric Yang-Mills theory with gauge group SU (N) (N ≥ 3) is believed to have two exactly marginal deformations which break the supersymmetry to N = 1. We discuss the construction of the string theory dual to these deformations, in the supergravity approximation, in a perturbation series around the AdS 5 × S 5 solution. We construct explicitly the deformed solution at second order in the deformation. We show that deformations which are marginal but not exactly marginal lead to a non-conformal solution with a logarithmically running coupling constant. Surprisingly, at third order in the deformation we find the same beta functions for the couplings in field theory and in supergravity, suggesting that the leading order beta functions (or anomalous dimensions) do not depend on the gauge coupling (the coefficient is not renormalized).
The large N limit of superconformal field theories and supergravity
Arxiv preprint hep-th/9711200, 1997
We show that the large N limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of Anti-deSitter spacetimes, spheres and other compact manifolds. This is shown by taking some branes in the full M/string theory and then taking a low energy limit where the field theory on the brane decouples from the bulk. We observe that, in this limit, we can still trust the near horizon geometry for large N . The enhanced supersymmetries of the near horizon geometry correspond to the extra supersymmetry generators present in the superconformal group (as opposed to just the super-Poincare group). The 't Hooft limit of 3+1 N = 4 super-Yang-Mills at the conformal point is shown to contain strings: they are IIB strings. We conjecture that compactifications of M/string theory on various Anti-deSitter spacetimes is dual to various conformal field theories. This leads to a new proposal for a definition of M-theory which could be extended to include five non-compact dimensions.
On exactly marginal deformations of Script N = 4 SYM and Type IIB Supergravity on AdS 5 × S 5
Journal of High Energy Physics, 2002
N = 4 supersymmetric Yang-Mills theory with gauge group SU (N ) (N ≥ 3) is believed to have two exactly marginal deformations which break the supersymmetry to N = 1. We discuss the construction of the string theory dual to these deformations, in the supergravity approximation, in a perturbation series around the AdS 5 × S 5 solution. We construct explicitly the deformed solution at second order in the deformation. We show that deformations which are marginal but not exactly marginal lead to a non-conformal solution with a logarithmically running coupling constant. Surprisingly, at third order in the deformation we find the same beta functions for the couplings in field theory and in supergravity, suggesting that the leading order beta functions (or anomalous dimensions) do not depend on the gauge coupling (the coefficient is not renormalized).
Dilatation operator and the Super Yang-Mills duals of open strings on AdS giant gravitons
Journal of High Energy Physics, 2006
We study the one-loop anomalous dimensions of the Super Yang-Mills dual operators to open strings ending on AdS giant gravitons. AdS giant gravitons have no upper bound for their angular momentum and we represent them by the contraction of scalar fields, carrying the appropriate R-charge, with a totally symmetric tensor. We represent the open string motion along AdS directions by appending to the giant graviton operator a product of fields including covariant derivatives. We derive a bosonic lattice Hamiltonian that describes the mixing of these excited AdS giants operators under the action of the one-loop dilatation operator of N = 4 SYM. This Hamiltonian captures several intuitive differences with respect to the case of sphere giant gravitons. A semiclassical analysis of the Hamiltonian allows us to give a geometrical interpretation for the labeling used to describe the fields products appended to the AdS giant operators. It also allows us to show evidence for the existence of continuous bands in the Hamiltonian spectrum.
Softly-Broken {\cal N} = 4 Supersymmetry in the Large-N Limit
2000
We calculate the exact values of the holomorphic observables of N = 4 supersymmetric SU(N) Yang-Mills theory deformed by mass terms which preserve N = 1 SUSY. These include the chiral condensates in each massive vacuum of the theory as well as the central charge which determines the tension of BPS saturated domain walls interpolating between these vacua. Several unexpected features emerge in the large-N limit, including anomalous modular properties under an SL(2, Z) duality group which acts on a complexification of the 't Hooft coupling λ = g 2 N/4π. We discuss our results in the context of the AdS/CFT correspondence.
On exactly marginal deformations of N = 4 SYM and type IIB supergravity on AdS5 × S5
Journal of High Energy Physics
N = 4 supersymmetric Yang-Mills theory with gauge group SU (N ) (N ≥ 3) is believed to have two exactly marginal deformations which break the supersymmetry to N = 1. We discuss the construction of the string theory dual to these deformations, in the supergravity approximation, in a perturbation series around the AdS 5 × S 5 solution. We construct explicitly the deformed solution at second order in the deformation. We show that deformations which are marginal but not exactly marginal lead to a non-conformal solution with a logarithmically running coupling constant. Surprisingly, at third order in the deformation we find the same beta functions for the couplings in field theory and in supergravity, suggesting that the leading order beta functions (or anomalous dimensions) do not depend on the gauge coupling (the coefficient is not renormalized).
Bulk gauge fields in AdS supergravity and supersingletons
We describe conformal operators living at the boundary of AdS d+1 in a general setting. Primary conformal operators at the threshold of the unitarity bounds of UIR's of O(d,2) correspond to singletons and massless fields in AdS d+1 , respectively. For maximal supersymmetric theories in AdS d+1 we describe "chiral" primary short supermultiplets and non-chiral primary long supermultiplets. Examples are exhibited which correspond to KK and string states. We give the general contribution of a primary conformal operator to the OPE and Green's functions of primary fields, which may be relevant to compute string corrections to the four-point supergraviton amplitude in Anti-de-Sitter space. Some aspects of the AdS d+1 /CFT correspondence, inspired by the original conjecture by Maldacena[1], and subsequently sharpened by Gubser, Klebanov, Polyakov and Witten , are considered in this paper 1 . The maximal supersymmetric case, corresponding to the horizon geometry of D3 branes in type IIB strings, is considered as basic example.