A Universal result on central charges in the presence of double trace deformations

By S. Gubser, I. Klebanov. 2002

254 citations recorded by the source corpus.

We study large N conformal field theories perturbed by relevant double-trace deformations. Using the auxiliary field trick, or Hubbard-Stratonovich transformation, we show that in the infrared the theory flows to another CFT. The generating functionals of planar correlators in the ultraviolet and infrared CFT’s are shown to be related by a Legendre transform. Our main result is a universal expression for the difference of the scale anomalies between the ultraviolet and infrared fixed points, which is of order 1 in the large N expansion. Our computations are entirely field theoretic, and the results are shown to agree with predictions from AdS/CFT. We also remark that a certain two-point function can be computed for all energy scales on both sides of the duality, with full agreement between the two and no scheme dependence.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/c49918e6bac0bee72845bebce1fee242ebf9819e

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The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. S. Hartnoll
2. J. Maldacena
3. D. Stanford
4. S. Sachdev
5. R. Myers
6. D. Harlow
7. T. Takayanagi
8. Thomas Hartman

In Nuclear and High Energy Physics

1. J. Maldacena
2. S. Hartnoll
3. R. Myers
4. S. Sachdev
5. S. Giombi
6. T. Takayanagi
7. D. Stanford
8. D. Harlow

Citations in the corpus

• Boundary conditions and dualities: vector fields in AdS/CFT (2006, methodology): “As conjectured in [30] and discussed in detail in [10], the bulk theory with β = 0 boundary conditions is dual to a CFT for which the generating functional for planar diagrams is related to that of the α = 0 theory.”
• F-theorem without supersymmetry (2011, methodology): “As in [47] we proceed through a Hubbard-Stratonovich transformation.”
• Higher spin gauge theory and holography: the three-point functions (2009, methodology): “In some cases, there are superficial divergences due to the nonlocal nature of Vasiliev theory, and suitable regularization in the bulk will 2 The correlation function of the ∆ = 1 scalar operator in the large N limit may also be understood in terms of the ∆ = 2 case using the Legendre transform [29”
• AdS description of induced higher-spin gauge theory (2013, background): “For s = 0 this expression agrees with the results in [7, 8, 10].”
• Holographic c-theorems in arbitrary dimensions (2010, background): “Further evidence for Cardy’s proposed c-theorem and our conjecture above can be found by examining RG flows induced by double-trace operators [67, 68].”
• Notes on the complex Sachdev-Ye-Kitaev model (2019, methodology): “We note that this procedure is similar to that used to compute the influence of double trace operators on the free energy in the AdS/CFT correspondence [40–45].”
• An apologia for firewalls (2013, methodology): “Much useful technology for doing so has been developed by the AdS/CFT community [56, 57, 58], though it refers only to semiclassical AdS physics.”
• Black hole determinants and quasinormal modes (2009, background): “Exceptions to this last statement include [4, 5, 6] who studied an effect due to the determinant term in pure Anti-de Sitter space.”
• Higher spins in AdS5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT (2014, unknown): “In the context of AdS/CFT it appeared in the context of the discussion of the bulk counterpart of a “double trace” deformation of the boundary CFT (see [11–14, 9, 10, 1]).”
• Holographic Quantum Matter (2016, background): “It is a general fact about large N conformal field theories that such an irrelevant double trace deformation induces a flow leading to a new UV fixed point theory [309].”
• Interpolating between a and F (2014, background): “Then one can show that, for ∆ < d/2, the perturbed CFT flows to a large N IR fixed point where O∆ ∼ σ has dimension d−∆ +O(1/N) [21, 69].”
• On Higher Spin Gauge Theory and the Critical O(N) Model (2011, methodology): “In some sense our arguments are an extension of the Legendre transform relating the two boundary conditions [9, 10] to all order in 1/N .”
• Correlation functions of large N Chern-Simons-Matter theories and bosonization in three dimensions (2012, background): “between the two bosonic (fermionic) theories is just a different choice of boundary conditions for the bulk scalar field which is dual to J ; in the classical gravity limit this is equivalent to a Legendre transform [11, 12, 13].”
• SL(2;Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry (2003, result): “This work was supported in part by NSF Grant PHY-0070928.”