Galilean Conformal Algebras and AdS/CFT

By Arjun Bagchi, Rajesh Gopakumar. 2009

400 citations recorded by the source corpus.

Non-relativistic versions of the AdS/CFT conjecture have recently been investigated in some detail. These have primarily been in the context of the Schrodinger symmetry group. Here we initiate a study based on a different non-relativistic conformal symmetry: one obtained by a parametric contraction of the relativistic conformal group. The resulting Galilean conformal symmetry has the same number of generators as the relativistic symmetry group and thus is different from the Schrodinger group (which has fewer). One of the interesting features of the Galilean Conformal Algebra is that it admits an extension to an infinite dimensional symmetry algebra (which can potentially be dynamically realised). The latter contains a Virasoro-Kac-Moody subalgebra. We comment on realisations of this extended symmetry in a boundary field theory. We also propose a somewhat unusual geometric structure for the bulk gravity dual to any realisation of this symmetry. This involves taking a Newton-Cartan like limit of Einstein's equations in anti de Sitter space which singles out an AdS2 comprising of the time and radial direction. The infinite dimensional Virasoro extension is identified with the asymptotic isometries of this AdS2.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/c455d5bf19e422d99eadcc1ea031bdc2997a8fd9

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In Geometry and Topology

1. B. Oblak
2. Marika Taylor
3. R. Basu
4. Aditya Mehra
5. Ashish Kakkar
6. J. Hartong
7. Shankhadeep Chakrabortty
8. Pulastya Parekh

In Mathematical Physics

1. Marika Taylor
2. S. Hartnoll
3. Joaquim Gomis
4. J. Hartong
5. M. Rangamani
6. R. Basu
7. Aditya Mehra
8. Ashish Kakkar

In Nuclear and High Energy Physics

1. J. Hartong
2. N. Obers
3. Marika Taylor
4. Eric Bergshoeff
5. Ziqi Yan
6. Jan Rosseel
7. S. Hartnoll
8. Arjun Bagchi

Citations in the corpus

• Gravity and hydrodynamics: lectures on the fluid-gravity correspondence (2009, background): “This scaling limit reveals an interesting structure in the fluid equations—they are scale invariant under a new scaling symmetry, which is the Galilean conformal algebra discussed recently in [117].”
• Tensionless strings and Galilean Conformal Algebra (2013, background): “One can either work in terms of the dynamical connection [4, 30], or in terms”
• Strings with non-relativistic conformal symmetry and limits of the AdS/CFT correspondence (2018, background): “It is known that the GCA can be obtained from two copies of the Virasoro algebra via a contraction [21].”
• Carroll versus Galilei gravity (2017, background): “There exists another approach, initiated in [7], where not only the boundary QFT is non-relativistic but also the String Theory.”
• Flat holography: aspects of the dual field theory (2016, methodology): “But before that we would like to draw inspiration from a similar construction for the non-relativistic limit performed in [26].”
• Lifshitz holography (2015, methodology): “In [153, 154] it was proposed that one could take non-relativistic limits of AdS/CFT to obtain holographic dualities between bulk Newton-Cartan theories and boundary Galilean conformal field theories.”
• Lectures on holographic methods for condensed matter physics (2009, background): “[31] for a ‘massless’ (nonextended) Galilean algebra that may be of physical interest.”
• Notes on the BMS group in three dimensions: I. Induced representations (2014, background): “It is also isomorphic to the infinite-dimensional extension of the Galilean conformal algebra in two dimensions, gca2 [61–63].”
• Gauging the Carroll algebra and ultra-relativistic gravity (2015, background): “In 3 bulk dimensions it has been shown that the BMS algebra is isomorphic to the 2-dimensional Galilean conformal algebra [55, 56] (which is a contraction of the relativistic conformal group [57]).”
• Tensionless strings from worldsheet symmetries (2015, background): “which lead to current-algebra like commutators with the rest of the algebra [16].”
• BMS/GCA redux: towards flatspace holography from non-relativistic symmetries (2012, neutral): “1.1 Flat Space Holography 1 1.2 Galilean Conformal Algebra 2 1.3 An aside: Non-relativistic Hydrodynamics 3 1.4 Outline of the paper 3”