Much of my work since 1996 has focused on the exact relations between quantum field theories in four and three space-time dimensions, and higher dimensional theories which include gravity. My work on thermodynamics and absorption cross-sections by stacks of extended objects called D-branes paved the way to the formulation of the Anti-de Sitter/Conformal field Theory (AdS/CFT) correspondence. I made many contributions to the formulation of the “AdS/CFT dictionary,” which relates scaling dimensions and correlation functions in strongly interacting field theory to semi-classical dynamics in AdS space. My collaborators and I have also constructed a tractable gravitational description of a gauge theory which is nearly conformal at short distances but exhibits color confinement at long distances.
In flat space there are problems with interacting fields of spin greater than two, but Mikhail Vasiliev and his collaborators have succeeded in constructing consistent interacting higher-spin theories in Anti-de Sitter space. These theories necessarily include gravity (spin two particles). In a 2002 paper, Alexander Polyakov and I conjectured that the simplest of Vasiliev's theories in 4-dimensional AdS space is dual, in the sense of the AdS/CFT correspondence, to O(N) symmetric theories of scalar fields in three dimensions. These field theories are very well-known; they generalize the theories that describe second-order phase transitions observed in real world, like the water-vapor critical point. They are rather simple because the basic fields are N-dimensional vectors rather than N by N matrices. By now there is considerable evidence that the conjecture we made in 2002 is correct. Notably, this provides a purely bosonic example of exact AdS/CFT correspondence (unlike the many earlier examples, it does not rely on supersymmetry). My most recent papers with Simone Giombi and others describe how the higher spin AdS/CFT correspondence works at one loop.
In 2011 I was involved in proposing a positive quantity that decreases along any renormalization group flow from one three-dimensional CFT to another: it is minus the logarithm of the path integral on the three-dimensional sphere. This quantity is related to quantum entanglement entropy which has been the subject of much recent work by me and many others.
- I.R. Klebanov and A.A. Tseytlin, "Entropy of near-extremal black p-branes," Nucl. Phys. B475 (1996) 164, hep-th/9604089.
- I.R. Klebanov, "World volume approach to absorption by nondilatonic branes," Nucl. Phys. B496 (1997) 231, hep-th/9702076.
- S.S. Gubser, I.R. Klebanov, and A.M. Polyakov, "Gauge theory correlators from noncritical string theory," Phys. Lett. B428 (1998) 105, hep-th/9802109
- I.R. Klebanov and E. Witten, "Superconformal Field Theory on Threebranes at a Calabi-Yau Singularity," Nucl. Phys. B536 (1998) 199, hep-th/9807080
- I.R. Klebanov and E. Witten, "AdS/CFT Correspondence and Symmetry Breaking," Nucl. Phys. B556 (1999) 89, hep-th/9905104
- I.R. Klebanov and A.A. Tseytlin, "Gravity Duals of Supersymmetric SU(N)xSU(N+M) Gauge Theories," Nucl. Phys. B578 (2000) 123, hep-th/0002159
- I.R. Klebanov and M. Strassler, "Supergravity and a Confining Gauge Theory: Duality Cascades and Chiral Symmetry Breaking Resolution of Naked Singularities," JHEP 0008 (2000) 052, hep-th/0007191
- S.S. Gubser, I.R. Klebanov, and A.M. Polyakov, "A Semiclassical limit of the gauge/string correspondence," Nucl. Phys. B636(2002) 99, hep-th/0204051
- I.R. Klebanov and A.M. Polyakov, "AdS Dual of the Critical O(N) Vector Model," Phys. Lett. B550 (2002) 213, hep-th/0210114
- I.R. Klebanov and J.M. Maldacena, "Solving Quantum Field Theories via Curved Spacetimes," Physics Today 62 (2009) 28
- D. Jafferis, I.R. Klebanov, S. Pufu and B. Safdi, "Towards the F-Theorem: N=2 Theories on the Three-Sphere," JHEP 1106 (2011) 102, ArXiv:1103.1181
- I.R. Klebanov, S. Pufu and B. Safdi, "Towards the F-Theorem: N=2 Theories on the Three-Sphere," JHEP 1110 (2011) 038, ArXiv:1105.4598
- I.R. Klebanov, S. Pufu, S. Sachdev and B. Safdi, "Entanglement Entropy of 3-d Conformal Gauge Theories with Many Flavors," JHEP 1205 (2012) 036, ArXiv:1112.534
- S. Giombi and I.R. Klebanov, "One Loop Tests of Higher Spin AdS/CFT," JHEP 1312 (2013) 068, ArXiv:1308.2337
S. Giombi, I.R. Klebanov and B. Safdi, "Higher Spin AdSd+1d+1/CFTdd at One Loop," ArXiv: 1401.0825