Triangle Seminars
Wednesday, 17 Oct 2018
Non-planar Scattering Amplitude - Wilson Loop Duality
Alexander Tumanov
(Tel Aviv U.)
Abstract:
Higher order corrections in the 1/N expansion to scattering amplitudes come from the diagrams with higher genus. One way to address these non-trivial topologies is to view them as planar objects glued into non-planar configurations. They can then be "cut" across all the cycles of the corresponding Riemann surface, fixing the momentum flowing in each cycle. This procedure results in a planar object that belongs to a representation of the modular group of the Riemann surface in question. Various techniques developed for the planar amplitudes can be generalized to these cut non-planar ones. We will investigate the scattering amplitude — Wilson loop duality, specifically focusing on the case of the first non-planar correction, 1/N double trace amplitude, which has the topology of a cylinder. It’s dual space interpretation is a correlator of two infinite Wilson lines subject to a periodicity constraint. We will confirm this duality by a weak coupling perturbative calculation and a strong coupling string worldsheet one. This will allow us to construct the non-planar loop integrands and the BCFW recursion relation they satisfy, as well as to find an interpretation of the dual conformal symmetry in the non-planar sector, which was previously thought to be broken by 1/N corrections. Lastly, we will discuss this result in the framework of the Wilson Loop OPE approach, which allows one to compute expectation values of Wilson loops at any value of the coupling in the form of an expansion around the collinear limit. We claim that this approach can be directly applied to cut non-planar scattering amplitudes, as well as the N=4 SYM form factors, whose dual space interpretation is remarkably similar to the one of the 1/N amplitude correction.
Higher order corrections in the 1/N expansion to scattering amplitudes come from the diagrams with higher genus. One way to address these non-trivial topologies is to view them as planar objects glued into non-planar configurations. They can then be "cut" across all the cycles of the corresponding Riemann surface, fixing the momentum flowing in each cycle. This procedure results in a planar object that belongs to a representation of the modular group of the Riemann surface in question. Various techniques developed for the planar amplitudes can be generalized to these cut non-planar ones. We will investigate the scattering amplitude — Wilson loop duality, specifically focusing on the case of the first non-planar correction, 1/N double trace amplitude, which has the topology of a cylinder. It’s dual space interpretation is a correlator of two infinite Wilson lines subject to a periodicity constraint. We will confirm this duality by a weak coupling perturbative calculation and a strong coupling string worldsheet one. This will allow us to construct the non-planar loop integrands and the BCFW recursion relation they satisfy, as well as to find an interpretation of the dual conformal symmetry in the non-planar sector, which was previously thought to be broken by 1/N corrections. Lastly, we will discuss this result in the framework of the Wilson Loop OPE approach, which allows one to compute expectation values of Wilson loops at any value of the coupling in the form of an expansion around the collinear limit. We claim that this approach can be directly applied to cut non-planar scattering amplitudes, as well as the N=4 SYM form factors, whose dual space interpretation is remarkably similar to the one of the 1/N amplitude correction.
Posted by: QMW
Twisting and localization in supergravity: equivariant cohomology of BPS black holes
📍 London
Imtak Jeon
(KCL)
Abstract:
We develop the formalism of supersymmetric localization in supergravity using the deformed BRST algebra defined in the presence of a supersymmetric background as recently formulated in arxiv:1806.03690. The gravitational functional integral localizes onto the cohomology of a global supercharge Q, obeying Q2=H, where H is a global symmetry of the background. Our construction naturally produces a twisted version of supergravity whenever supersymmetry can be realized off-shell. We present the details of the twisted graviton multiplet and ghost fields for the superconformal formulation of four-dimensional N=2 supergravity. As an application of our formalism, we systematize the computation of the exact quantum entropy of supersymmetric black holes. In particular, we compute the one-loop determinant of the QV deformation operator for the off-shell fluctuations of the Weyl multiplet around the AdS2×S2 saddle. This result, which is consistent with the corresponding large-charge on-shell analysis, is needed to complete the first-principles computation of the quantum entropy.
We develop the formalism of supersymmetric localization in supergravity using the deformed BRST algebra defined in the presence of a supersymmetric background as recently formulated in arxiv:1806.03690. The gravitational functional integral localizes onto the cohomology of a global supercharge Q, obeying Q2=H, where H is a global symmetry of the background. Our construction naturally produces a twisted version of supergravity whenever supersymmetry can be realized off-shell. We present the details of the twisted graviton multiplet and ghost fields for the superconformal formulation of four-dimensional N=2 supergravity. As an application of our formalism, we systematize the computation of the exact quantum entropy of supersymmetric black holes. In particular, we compute the one-loop determinant of the QV deformation operator for the off-shell fluctuations of the Weyl multiplet around the AdS2×S2 saddle. This result, which is consistent with the corresponding large-charge on-shell analysis, is needed to complete the first-principles computation of the quantum entropy.
Posted by: KCL
Aspects of de Sitter spacetimes
Dionysios Anninos
(Amsterdam)
Abstract:
We overview some aspects of asymptotically de Sitter spacetimes at the classical and quantum level. We discuss some features of the late time de Sitter wavefunction. We briefly touch upon some properties of the relation between de Sitter space and Euclidean conformal theories, broadly referred to as the dS/CFT correspondence. Finally, time permitting, we will discuss some similarities and differences between the cosmological dS horizon and a more standard black hole horizon.
We overview some aspects of asymptotically de Sitter spacetimes at the classical and quantum level. We discuss some features of the late time de Sitter wavefunction. We briefly touch upon some properties of the relation between de Sitter space and Euclidean conformal theories, broadly referred to as the dS/CFT correspondence. Finally, time permitting, we will discuss some similarities and differences between the cosmological dS horizon and a more standard black hole horizon.
Posted by: QMW