Triangle Seminars
Tuesday, 18 May 2021
The hazardous landscape of Affinesia
Jose Beltran Jimenez
(Salamanca University)
Abstract:
The standard formulation of General Relativity is based on a geometrical framework where the spacetime manifold is endowed with a Lorentzian metric and its associated Levi-Civita connection. Since the affine structure is independent of the metric, it is possible to extend this geometrical set-up to allow for more general connections, thus giving rise to the metric-affine framework where the new actors are the torsion and the non-metricity. After discussing how these two objects can provide equivalent descriptions of GR, I will discuss how pathologies arise in modified theories of gravity along different directions in the metric-affine landscape.
[please email a.held@imperial.ac.uk for zoom link or password]
The standard formulation of General Relativity is based on a geometrical framework where the spacetime manifold is endowed with a Lorentzian metric and its associated Levi-Civita connection. Since the affine structure is independent of the metric, it is possible to extend this geometrical set-up to allow for more general connections, thus giving rise to the metric-affine framework where the new actors are the torsion and the non-metricity. After discussing how these two objects can provide equivalent descriptions of GR, I will discuss how pathologies arise in modified theories of gravity along different directions in the metric-affine landscape.
[please email a.held@imperial.ac.uk for zoom link or password]
Posted by: IC
Thursday, 20 May 2021
Integrated four-point correlators in N=4 super Yang-Mills.
Congkao Wen
(QMUL)
Abstract:
We will study the correlation function of four superconformal primaries in N=4 super Yang-Mills (SYM) with SU(N) gauge group. Recently, very powerful methods have been developed to compute this correlator at finite coupling based on a new concept of integrated correlators, which are defined by integrating the correlator over spacetime coordinates with suitable integration measures. The integrated correlators can be computed using supersymmetric localisation. We will mostly focus on one of the integrated correlators. An exact expression was found for this integrated correlator for arbitrary values of coupling and N. The integrated correlator can be expressed as a two-dimensional lattice sum, which manifests the SL(2, Z) modular invariance of N=4 SYM. Furthermore, the result obeys an elegant Laplace-difference equation that relates the correlator of SU(N) theory with those of SU(N-1) and SU(N+1) theories. In perturbation, the formula is checked to be consistent with known results from more standard methods. Finally, one can reconstruct the unintegrated correlator with finite coupling for first few orders in large-N expansion, the results are shown to agree with known type IIB superstring amplitudes due to AdS/CFT duality. This talk will be mainly based on arxiv.org/abs/2102.09537 (a short version can be found at arxiv.org/abs/2102.08305). –- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. The link will be emailed on Tuesday.
We will study the correlation function of four superconformal primaries in N=4 super Yang-Mills (SYM) with SU(N) gauge group. Recently, very powerful methods have been developed to compute this correlator at finite coupling based on a new concept of integrated correlators, which are defined by integrating the correlator over spacetime coordinates with suitable integration measures. The integrated correlators can be computed using supersymmetric localisation. We will mostly focus on one of the integrated correlators. An exact expression was found for this integrated correlator for arbitrary values of coupling and N. The integrated correlator can be expressed as a two-dimensional lattice sum, which manifests the SL(2, Z) modular invariance of N=4 SYM. Furthermore, the result obeys an elegant Laplace-difference equation that relates the correlator of SU(N) theory with those of SU(N-1) and SU(N+1) theories. In perturbation, the formula is checked to be consistent with known results from more standard methods. Finally, one can reconstruct the unintegrated correlator with finite coupling for first few orders in large-N expansion, the results are shown to agree with known type IIB superstring amplitudes due to AdS/CFT duality. This talk will be mainly based on arxiv.org/abs/2102.09537 (a short version can be found at arxiv.org/abs/2102.08305). –- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. The link will be emailed on Tuesday.
Posted by: andrea