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15
From Large N Nonplanar Anomalous Dimensions to Open Spring Theory,” [arXiv:1111.1058 [hepth
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Geometries from Young Diagrams
, 2008
"... Type IIB string theory on spacetimes that are asymptotically AdS5×S5 can be defined using four dimensional N = 4 super YangMills theory. Six of the dimensions of the string theory are holographically reconstructed in the YangMills theory. In this article we study how these dimensions and local p ..."
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Cited by 16 (6 self)
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Type IIB string theory on spacetimes that are asymptotically AdS5×S5 can be defined using four dimensional N = 4 super YangMills theory. Six of the dimensions of the string theory are holographically reconstructed in the YangMills theory. In this article we study how these dimensions and local physics in these dimensions emerge. We reorganize the dynamics of the 1 BPS sector of the field theory by rewriting it in terms 2 of Schur polynomials. The Young diagram labeling of these polynomials can be viewed as a book keeping device which summarizes how the operator is constructed. We show that aspects of the geometry of the extra holographic dimensions are captured very naturally by the Young diagram. Gravitons which are localized at a specific position
Exact MultiRestricted Schur Polynomial Correlators
, 2008
"... We derive a product rule satisfied by restricted Schur polynomials. We focus mostly on the case that the restricted Schur polynomial is built using two matrices, although our analysis easily extends to more than two matrices. This product rule allows us to compute exact multipoint correlation func ..."
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Cited by 2 (0 self)
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We derive a product rule satisfied by restricted Schur polynomials. We focus mostly on the case that the restricted Schur polynomial is built using two matrices, although our analysis easily extends to more than two matrices. This product rule allows us to compute exact multipoint correlation functions of restricted Schur polynomials, in the free field theory limit. As an example of the use of our formulas, we compute two point functions of certain single trace operators built using two matrices and three point functions of certain restricted Schur polynomials, exactly, in the free field theory limit. Our results suggest that gravitons become strongly coupled at sufficiently high energy, while the restricted Schur polynomials for totally antisymmetric representations remain weakly interacting at these energies. This is in perfect accord with the halfBPS (single matrix) results of hepth/0512312. Finally, by studying the interaction of two restricted Schur polynomials we suggest a physical interpretation for the labels of the restricted Schur polynomial: the composite operator χR,(rn,rm)(Z, X)
Correlators of operators . . .
, 2009
"... Correlation functions of operators with a conformal dimension of O(N²) are not well approximated by the planar limit. The nonplanar diagrams, which in the bulk spacetime correspond to string loop corrections, are enhanced by huge combinatorial factors. In this article we show how these loop corre ..."
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Correlation functions of operators with a conformal dimension of O(N²) are not well approximated by the planar limit. The nonplanar diagrams, which in the bulk spacetime correspond to string loop corrections, are enhanced by huge combinatorial factors. In this article we show how these loop corrections can be resummed. As a typical example of our results, in the halfBPS background of M maximal giant gravitons we find the usual 1/N expansion is replaced by a 1/(M + N) expansion. Further, we find that there is a simple exact relationship between amplitudes computed in the trivial background and amplitudes computed in the background of M maximal giant gravitons. Finally, we also find strong evidence for the BMNtype sectors suggested in arXiv:0801.4457. The decoupling limit of arXiv:0801.4457 captures the decoupled low energy world volume theory of the intersecting giant graviton system and this theory is weakly coupled even when the original N = 4 super YangMills theory is strongly coupled.
Correlators of operators with a large . . .
, 2009
"... Correlation functions of operators with a conformal dimension of O(N²) are not well approximated by the planar limit. The nonplanar diagrams, which in the bulk spacetime correspond to string loop corrections, are enhanced by huge combinatorial factors. In this article we show how these loop corre ..."
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Correlation functions of operators with a conformal dimension of O(N²) are not well approximated by the planar limit. The nonplanar diagrams, which in the bulk spacetime correspond to string loop corrections, are enhanced by huge combinatorial factors. In this article we show how these loop corrections can be resummed. As a typical example of our results, in the halfBPS background of M maximal giant gravitons we find the usual 1/N expansion is replaced by a 1/(M + N) expansion. Further, we find that there is a simple exact relationship between amplitudes computed in the trivial background and amplitudes computed in the background of M maximal giant gravitons. Finally, we also find strong evidence for the BMNtype sectors suggested in arXiv:0801.4457. The decoupling limit of arXiv:0801.4457 captures the decoupled low energy world volume theory of the intersecting giant graviton system and this theory is weakly coupled even when the original N = 4 super YangMills theory is strongly coupled.
Correlators in nontrivial backgrounds
, 2009
"... Operators in N = 4 super YangMills theory with an Rcharge of O(N²) are dual to backgrounds which are asymtotically AdS5×S 5. In this article we develop efficient techniques that allow the computation of correlation functions in these backgrounds. We find that (i) contractions between fields in t ..."
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Operators in N = 4 super YangMills theory with an Rcharge of O(N²) are dual to backgrounds which are asymtotically AdS5×S 5. In this article we develop efficient techniques that allow the computation of correlation functions in these backgrounds. We find that (i) contractions between fields in the string words and fields in the operator creating the background are the field theory accounting of the new geometry, (ii) correlation functions of probes in these backgrounds are given by the free field theory contractions but with rescaled propagators and (iii) in these backgrounds there are no open string excitations with their special end point interactions; we have only closed string excitations.
Wits, 2050,
, 710
"... Abstract: We develop techniques to compute the oneloop anomalous dimensions of operators in the N = 4 super YangMills theory that are dual to open strings ending on boundstates of sphere giant gravitons. Our results, which are applicable to excitations involving an arbitrary number of open strings ..."
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Abstract: We develop techniques to compute the oneloop anomalous dimensions of operators in the N = 4 super YangMills theory that are dual to open strings ending on boundstates of sphere giant gravitons. Our results, which are applicable to excitations involving an arbitrary number of open strings, generalize the single string results of hepth/0701067. The open strings we consider carry angular momentum on an S 3 embedded in the S 5 of the AdS5×S 5 background. The problem of computing the one loop anomalous dimensions is replaced with the problem of diagonalizing an interacting Cuntz oscillator Hamiltonian. Our Cuntz oscillator dynamics illustrates how the ChanPaton factors for open strings propagating on multiple branes can arise dynamically.
The AdS5 × S 5 superstrings in the generalized lightcone gauge
, 2006
"... The κsymmetryfixed GreenSchwarz action in the AdS5 × S5 background is treated canonically in a version of the lightcone gauge. After reviewing the generalized lightcone gauge for a bosonic sigma model, we present the Hamiltonian dynamics of the GreenSchwarz action by using the transverse degre ..."
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The κsymmetryfixed GreenSchwarz action in the AdS5 × S5 background is treated canonically in a version of the lightcone gauge. After reviewing the generalized lightcone gauge for a bosonic sigma model, we present the Hamiltonian dynamics of the GreenSchwarz action by using the transverse degrees of freedom. The remaining fermionic constraints are all second class, which we treat by the Dirac bracket. Upon quantization, all of the transverse coordinates are inevitably noncommutative.