Triangle Seminars
Tuesday, 17 Oct 2017
Renormalization of total sets of states into generalized bases with a resolution of the identity: a cooperative game theory approach
Apostolos Vourdas
(Bradford)
Abstract:
A total set of states for which we have no resolution of the identity (a 'pre-basis'), is considered
in a finite dimensional Hilbert space. A dressing formalism renormalizes them into density matrices
which resolve the identity, and makes them a 'generalized basis', which is practically useful. The
dresssing mechanism is inspired by Shapley's methodology in cooperative game theory, and it uses
Moebius transforms. There is non-independence and redundancy in these generalized bases, which is
quantified with a Shannon type of entropy. Due to this redundancy, calculations based on generalized
bases, are sensitive to physical changes and robust in the presence of noise. For example, the
representation of an arbitrary vector in such generalized bases, is robust when noise is inserted in
the coefficients. Also in a physical system with ground state which changes abruptly at some value
of the coupling constant, the proposed methodology detects such changes, even when noise is added
to the parameters in the Hamiltonian of the system.
A total set of states for which we have no resolution of the identity (a 'pre-basis'), is considered
in a finite dimensional Hilbert space. A dressing formalism renormalizes them into density matrices
which resolve the identity, and makes them a 'generalized basis', which is practically useful. The
dresssing mechanism is inspired by Shapley's methodology in cooperative game theory, and it uses
Moebius transforms. There is non-independence and redundancy in these generalized bases, which is
quantified with a Shannon type of entropy. Due to this redundancy, calculations based on generalized
bases, are sensitive to physical changes and robust in the presence of noise. For example, the
representation of an arbitrary vector in such generalized bases, is robust when noise is inserted in
the coefficients. Also in a physical system with ground state which changes abruptly at some value
of the coupling constant, the proposed methodology detects such changes, even when noise is added
to the parameters in the Hamiltonian of the system.
Posted by: KCL
Wednesday, 18 Oct 2017
On the exact interpolating function in ABJ theory
📍 London
Andrea Cavaglia
(KCL)
Abstract:
I will discuss integrability in the context of planar AdS4/CFT3,
where the CFT is the so-called ABJ model depending on two t'Hooft couplings.
When the two couplings are equal, this reduces to the ABJM theory, whose integrable structure is well understood
but depends on an unspecified interpolating function of the coupling.
I will motivate a proposal that the most general ABJ case is also integrable,
and that the two coupling constants l1 and l2 recombine into a single
interpolating function h( l1 , l2 ) , so that the spectrum is a function of h only.
Extending and idea by N. Gromov and G. Sizov on the ABJM case,
an explicit conjecture for the form of h(l1, l2) wil be made, based on the comparison between
integrability and localization results.
The talk is based on the paper hep-th/1605.04888 with N. Gromov and F. Levkovich-Maslyuk.
I will discuss integrability in the context of planar AdS4/CFT3,
where the CFT is the so-called ABJ model depending on two t'Hooft couplings.
When the two couplings are equal, this reduces to the ABJM theory, whose integrable structure is well understood
but depends on an unspecified interpolating function of the coupling.
I will motivate a proposal that the most general ABJ case is also integrable,
and that the two coupling constants l1 and l2 recombine into a single
interpolating function h( l1 , l2 ) , so that the spectrum is a function of h only.
Extending and idea by N. Gromov and G. Sizov on the ABJM case,
an explicit conjecture for the form of h(l1, l2) wil be made, based on the comparison between
integrability and localization results.
The talk is based on the paper hep-th/1605.04888 with N. Gromov and F. Levkovich-Maslyuk.
Posted by: KCL
Thursday, 19 Oct 2017
AdS3/CFT_2 and F-Theory
Christopher Couzens
(King's Coll. London)
Abstract:
In this talk we consider holographic duals of F-theory solutions to 2d SCFT's. We approach the problem by classifying a particular class of solutions of type IIB supergravity with AdS_3 factors and varying axio-dilaton. The class of solutions we discuss consist of D3 and 7-brane configurations and naturally fall into the realm of F-theory. We prove that for (0,4) supersymmetry in 2d the solutions are essentially unique and we match the holographic central charges to field theory results. We comment on future directions, including AdS_3 solutions of F-theory, preserving different amounts of supersymmetry.
In this talk we consider holographic duals of F-theory solutions to 2d SCFT's. We approach the problem by classifying a particular class of solutions of type IIB supergravity with AdS_3 factors and varying axio-dilaton. The class of solutions we discuss consist of D3 and 7-brane configurations and naturally fall into the realm of F-theory. We prove that for (0,4) supersymmetry in 2d the solutions are essentially unique and we match the holographic central charges to field theory results. We comment on future directions, including AdS_3 solutions of F-theory, preserving different amounts of supersymmetry.
Posted by: QMW