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Correlation functions in holographic renormalization group flows,” Nucl. Phys
 Lett. B
"... We consider the holographic duality for a generic bulk theory of scalars coupled to gravity. By studying the fluctuations around Poincaré invariant backgrounds with nonvanishing scalars, with the scalar and metric boundary conditions considered as being independent, we obtain all one and twopoint ..."
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Cited by 17 (4 self)
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We consider the holographic duality for a generic bulk theory of scalars coupled to gravity. By studying the fluctuations around Poincaré invariant backgrounds with nonvanishing scalars, with the scalar and metric boundary conditions considered as being independent, we obtain all one and twopoint functions in the dual renormalization group flows of the boundary field theory. Operator and vev flows are explicitly distinguished by means of the physical condensates. The method is applied to the GPPZ and Coulomb branch flows, and field theoretical expectations are confirmed. Correlation Functions in Holographic Renormalization Group Flows 1 1
and WilsonLoop
, 2000
"... The renormalization group equations of the YangMills theory are examined in the noncritical string theory according to the framework of the holography. Under a simple ansatz for the tachyon, we could find several interesting solutions which are classified by the value of the tachyon potential at t ..."
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The renormalization group equations of the YangMills theory are examined in the noncritical string theory according to the framework of the holography. Under a simple ansatz for the tachyon, we could find several interesting solutions which are classified by the value of the tachyon potential at the vacuum. We show two typical, asymptoticfree solutions which are different in their infrared behaviors. For both types of solutions, we could obtain quarkconfinement potential from the Wilsonloop. The stability of the tachyon and the ZigZag symmetry are also discussed for these solutions. 1
Holographic Renormalization Group
, 2002
"... The holographic renormalization group (RG) is reviewed in a selfcontained manner. The holographic RG is based on the idea that the radial coordinate of a spacetime with asymptotically AdS geometry can be identified with the RG flow parameter of boundary field theory. After briefly discussing basic ..."
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The holographic renormalization group (RG) is reviewed in a selfcontained manner. The holographic RG is based on the idea that the radial coordinate of a spacetime with asymptotically AdS geometry can be identified with the RG flow parameter of boundary field theory. After briefly discussing basic aspects of the AdS/CFT correspondence, we explain how the concept of the holographic RG emerges from this correspondence. We formulate the holographic RG on the basis of the HamiltonJacobi equations for bulk systems of gravity and scalar fields, as introduced by de Boer, Verlinde and Verlinde. We then show that the equations can be solved with a derivative expansion by carefully extracting local counterterms from the generating functional of the boundary field theory. The calculational methods used to obtain the Weyl anomaly and scaling dimensions are presented and applied to the RG flow from the N = 4 SYM to an N = 1 superconformal fixed point discovered by Leigh and Strassler. We further discuss the relation between the holographic RG and the noncritical string theory and show that the structure of the holographic RG should persist beyond the supergravity approximation as a consequence of the renormalizability of the nonlinear σmodel action of noncritical strings. As a check, we investigate the holographic RG structure
Casimir Energy of 5D Electromagnetism and New Regularization Based on MinimalArea Principle
, 2008
"... We examine the Casimir energy of 5D electromagnetism from the recent standpoint. The bulk geometry is flat. The Z2 symmetry and periodic property, for the extra coordinate, are taken into account. After confirming the consistency with the past result, we do new things based on a new regularization. ..."
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We examine the Casimir energy of 5D electromagnetism from the recent standpoint. The bulk geometry is flat. The Z2 symmetry and periodic property, for the extra coordinate, are taken into account. After confirming the consistency with the past result, we do new things based on a new regularization. In the treatment of the divergences, we introduce IR and UV cutoffs and restrict the (4D momentum, extra coordinate)integral region. The regularized configuration is the sphere lattice, in the 4D continuum space, which changes along the extra coordinate. The change (renormalization flow) is specified by the minimal area principle; hence, this regularization configuration is stringlike. We do the analysis not in the KaluzaKlein expanded form but in a closed form. We do not use any perturbation. The formalism is based on the heatkernel approach using the position/momentum propagator. Interesting relations between the heat kernels and the P/M propagators are obtained, where we introduce the generalized P/M propagators. A useful expression of the Casimir energy, in terms of the P/M propagator, is obtained. The restricted region approach is replaced by the weightfunction approach in the latterhalf description. Its meaning, in relation to spacetime quantization, is argued. Finite Casimir energy is numerically obtained.
unknown title
, 2000
"... TMR9: Quantum aspects of gauge theories, supersymmetry and unification PROCEEDINGS The Holographic RG flow to conformal and nonconformal theory ∗ ..."
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TMR9: Quantum aspects of gauge theories, supersymmetry and unification PROCEEDINGS The Holographic RG flow to conformal and nonconformal theory ∗
unknown title
, 2000
"... TMR9: Quantum aspects of gauge theories, supersymmetry and unification PROCEEDINGS The Holographic RG flow to conformal and nonconformal theory ∗ ..."
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TMR9: Quantum aspects of gauge theories, supersymmetry and unification PROCEEDINGS The Holographic RG flow to conformal and nonconformal theory ∗
30 Progress of Theoretical Physics Supplement No. 152, 2003 Loop Effects in AdS/CFT and Beyond
"... Doubletrace operators which are relevant deformations of large N conformal field theories give rise to renormalization group flows that can be studied on both sides of the AdS/CFT duality. Oneloop calculations in AdS can be compared successfully to results derived in field theory using the Hubbar ..."
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Doubletrace operators which are relevant deformations of large N conformal field theories give rise to renormalization group flows that can be studied on both sides of the AdS/CFT duality. Oneloop calculations in AdS can be compared successfully to results derived in field theory using the HubbardStratonovich transformation. The calculations do not rely on supersymmetry, and they apply in any dimension, provided the original conformal field theory and its AdS dual are welldefined. A speculative idea is proposed for solving the cosmological constant problem based on nongravitational strings that become light as the universe expands. This is a summary of my talk presented at the NishinomiyaYukawa Symposium in Nishinomiya, Japan. It is based primarily on [S. S. Gubser and I. Mitra, hepth/0210093; S. S. Gubser and I. R. Klebanov, hepth/0212138]. The study of renormalization group flows in AdS/CFT3)–5) is a fairly welldeveloped subject, reviewed partially in Refs. 6), 7). In order to put my main topic — RG flows caused by doubletrace operators — in context, I will briefly re
TMR9: Quantum aspects of gauge theories, supersymmetry and unication PROCEEDINGS The Supergravity Dual of N=1 Super YangMills
"... Abstract: We present an exact supersymmetric solution of 5dimensional supergravity. We show that it represents the RG flow from N=4 SYM deformed with a mass term for the fermions to an IR N=1 super YangMills theory. We discuss the properties of the solution and we briefly comment on the fate of th ..."
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Abstract: We present an exact supersymmetric solution of 5dimensional supergravity. We show that it represents the RG flow from N=4 SYM deformed with a mass term for the fermions to an IR N=1 super YangMills theory. We discuss the properties of the solution and we briefly comment on the fate of the singularity. We also compare the supergravity results with the expectations of an N=1 SYM at strong coupling. 1.
unknown title
"... TMR9: Quantum aspects of gauge theories, supersymmetry and unification PROCEEDINGS The Holographic RG flow to conformal and nonconformal theories ..."
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TMR9: Quantum aspects of gauge theories, supersymmetry and unification PROCEEDINGS The Holographic RG flow to conformal and nonconformal theories