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476
Bethe Ansatz for Quantum Strings
, 2004
"... We propose Bethe equations for the diagonalization of the Hamiltonian of quantum strings on AdS5×S 5 at large string tension and restricted to certain large charge states from a closed su(2) subsector. The ansatz differs from the recently proposed all-loop gauge theory asymptotic Bethe ansatz by add ..."
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Cited by 281 (16 self)
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We propose Bethe equations for the diagonalization of the Hamiltonian of quantum strings on AdS5×S 5 at large string tension and restricted to certain large charge states from a closed su(2) subsector. The ansatz differs from the recently proposed all-loop gauge theory asymptotic Bethe ansatz by additional factorized scattering terms for the local excitations. We also show that our ansatz quantitatively reproduces everything that is currently known about the string spectrum of these states. Firstly, by construction, we recover the integral Bethe equations describing semiclassical spinning strings. Secondly, we explain how to derive the 1/J energy corrections of M-impurity BMN states, provide explicit, general formulae for both distinct and confluent mode numbers, and compare to asymptotic gauge theory. In the special cases M = 2, 3 we reproduce the results of direct quantization of Callan et al. Lastly, at large string tension and relatively small charge we recover the famous 2 4 √ n 2 λ asymptotics of massive string modes at level n. Remarkably, this behavior is entirely determined by the novel scattering terms. This is qualitatively consistent with the conjecture that these terms occur due to wrapping effects in gauge theory. Our
The factorized S-matrix of CFT/AdS
, 2004
"... We argue that the recently discovered integrability in the large-N CFT/AdS system is equivalent to diffractionless scattering of the corresponding hidden elementary excitations. This suggests that, perhaps, the key tool for finding the spectrum of this system is neither the gauge theory’s dilatati ..."
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Cited by 240 (7 self)
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We argue that the recently discovered integrability in the large-N CFT/AdS system is equivalent to diffractionless scattering of the corresponding hidden elementary excitations. This suggests that, perhaps, the key tool for finding the spectrum of this system is neither the gauge theory’s dilatation operator nor the string sigma model’s quantum Hamiltonian, but instead the respective factorized S-matrix. To illustrate the idea, we focus on the closed fermionic su(1|1) sector of the N = 4 gauge theory. We introduce a new technique, the perturbative asymptotic Bethe ansatz, and use it to extract this sector’s three-loop S-matrix from Beisert’s involved algebraic work on the three-loop su(2|3) sector. We then show that the current knowledge about semiclassical and near-plane-wave quantum strings in the su(2), su(1|1) and sl(2) sectors of AdS5 ×S 5 is fully consistent with the existence of a factorized S-matrix. Analyzing the available information, we find an intriguing relation between the three associated S-matrices. Assuming that the relation also holds in gauge theory, we derive the three-loop S-matrix of the sl(2) sector even though this sector’s dilatation operator is not yet known beyond one loop. The resulting
A new double-scaling limit of N = 4 super Yang-Mills theory and PP-wave strings, Nucl. Phys. B643
, 2002
"... The metric of a spacetime with a parallel plane (pp)-wave can be obtained in a certain limit of the space AdS 5 ×S 5. According to the AdS/CFT correspondence, the holographic dual of superstring theory on that background should be the analogous limit of N = 4 supersymmetric Yang-Mills theory. In thi ..."
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Cited by 146 (16 self)
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The metric of a spacetime with a parallel plane (pp)-wave can be obtained in a certain limit of the space AdS 5 ×S 5. According to the AdS/CFT correspondence, the holographic dual of superstring theory on that background should be the analogous limit of N = 4 supersymmetric Yang-Mills theory. In this paper we shall show that, contrary to widespread expectation, non-planar diagrams survive this limiting procedure in the gauge theory. Using matrix model techniques as well as combinatorial reasoning it is demonstrated that a subset of diagrams of arbitrary genus survives and that a non-trivial double scaling limit may be defined. We exactly compute two- and three-point functions of chiral primaries in this limit. We also carefully study certain operators conjectured to correspond to string excitations on the pp-wave background. We find non-planar linear mixing of these proposed operators, requiring their redefinition. Finally, we show that the redefined operators receive non-planar corrections to the planar one-loop anomalous dimension.
The complete one-loop dilatation operator of N = 4 super Yang-Mills theory,” hep-th/0307015
- N. Beisert and M. Staudacher, “The N
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Superstring interactions in a pp-wave background
- PHYS. REV. D 66, 086004
, 2002
"... We construct light-cone gauge superstring field theory in a pp-wave background with Ramond-Ramond flux. The leading term in the interaction Hamiltonian is determined up to an overall function of p + by requiring closure of the pp-wave superalgebra. The bosonic and fermionic Neumann matrices for this ..."
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Cited by 134 (6 self)
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We construct light-cone gauge superstring field theory in a pp-wave background with Ramond-Ramond flux. The leading term in the interaction Hamiltonian is determined up to an overall function of p + by requiring closure of the pp-wave superalgebra. The bosonic and fermionic Neumann matrices for this cubic vertex are derived, as is the interaction
Raamsdonk, “Matrix perturbation theory for M-theory on a pp-wave,” hep-th/0205185
"... In this paper, we study the matrix model proposed by Berenstein, Maldacena, and Nastase to describe M-theory on the maximally supersymmetric pp-wave. We show that the model may be derived directly as a discretized theory of supermembranes in the pp-wave background, or alternatively, from the dynamic ..."
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Cited by 133 (14 self)
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In this paper, we study the matrix model proposed by Berenstein, Maldacena, and Nastase to describe M-theory on the maximally supersymmetric pp-wave. We show that the model may be derived directly as a discretized theory of supermembranes in the pp-wave background, or alternatively, from the dynamics of D0-branes in type IIA string theory. We consider expanding the model about each of its classical supersymmetric vacua and note that for large values of the mass parameter µ, interaction terms are suppressed by powers of µ −1, so that the model may be studied in perturbation theory. We compute the exact spectrum about each of the vacua in the large µ limit and find the complete (infinite) set of BPS states, which includes states preserving 2, 4, 6, 8, or 16 supercharges. Through explicit perturbative calculations, we then determine the effective coupling that controls the perturbation expansion for large µ and estimate the range
Penrose limits, supergravity and brane dynamics
, 2002
"... Abstract. We investigate the Penrose limits of classical string and M-theory backgrounds. We prove that the number of (super)symmetries of a supergravity background never decreases in the limit. We classify all the possible Penrose limits of AdS ×S spacetimes and of supergravity brane solutions. We ..."
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Cited by 104 (7 self)
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Abstract. We investigate the Penrose limits of classical string and M-theory backgrounds. We prove that the number of (super)symmetries of a supergravity background never decreases in the limit. We classify all the possible Penrose limits of AdS ×S spacetimes and of supergravity brane solutions. We also present the Penrose limits of various other solutions: intersecting branes, supersymmetric black holes and strings in diverse dimensions, and cosmological models. We explore the Penrose limit of an isometrically embedded spacetime and find a generalisation to spaces with more than one time. Finally, we show that the Penrose limit is a large tension limit for all branes including those with fields of Born–Infeld type. Contents
Integrable Hamiltonian for classical strings on ADS5 × S 5
, 2004
"... We find the Hamiltonian for physical excitations of the classical bosonic string propagating in the AdS5 × S5 space-time. The Hamiltonian is obtained in a so-called uniform gauge which is related to the static gauge by a 2d duality transformation. The Hamiltonian is of the Nambu type and depends on ..."
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Cited by 102 (13 self)
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We find the Hamiltonian for physical excitations of the classical bosonic string propagating in the AdS5 × S5 space-time. The Hamiltonian is obtained in a so-called uniform gauge which is related to the static gauge by a 2d duality transformation. The Hamiltonian is of the Nambu type and depends on two parameters: a single S5 angular momentum J and the string tension λ. In the general case both parameters can be finite. The space of string states consists of short and long strings. In the sector of short strings the large J expansion with λ ′ = λ J2 fixed recovers the plane-wave Hamiltonian and higher-order corrections recently studied in the literature. In the strong coupling limit λ → ∞, J fixed, the energy of short strings scales as 4 √ λ while the energy of long strings scales as √ λ. We further show that the gauge-fixed Hamiltonian is integrable by constructing the corresponding Lax representation. We discuss some general properties of the monodromy matrix, and verify that the asymptotic behavior of the quasi-momentum perfectly agrees with the one
The SU(3) spin chain sigma model and string theory
- JHEP
, 2004
"... hep–th/0403139 ..."
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Strings on pp-waves and massive two dimensional field theories
"... We find a general class of pp-wave solutions of type IIB string theory such that the light cone gauge worldsheet lagrangian is that of an interacting massive field theory. When the light cone Lagrangian has (2,2) supersymmetry we can find backgrounds that lead to arbitrary superpotentials on the wor ..."
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Cited by 67 (3 self)
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We find a general class of pp-wave solutions of type IIB string theory such that the light cone gauge worldsheet lagrangian is that of an interacting massive field theory. When the light cone Lagrangian has (2,2) supersymmetry we can find backgrounds that lead to arbitrary superpotentials on the worldsheet. We consider situations with both flat and curved transverse spaces. We describe in some detail the background giving rise to the N = 2 sine Gordon theory on the worldsheet. Massive mirror symmetry relates it to the deformed CP 1 model (or sausage model) which seems to elude a purely supergravity target space interpretation. 1
