Twenty-Seventh Meeting of the North British Mathematical Physics Seminar

We will review integrability and the role of quantum group symmetries and their representations in the spectral problem of supersymmetric Yang-Mills theory, and the relevance for the AdS/CFT conjecture.

I will present a common algebraic setting for Q-operators and defects in the XXZ and sine-Gordon models and discuss the connection with the work of Bowcock, Corrigan and Zambon.

Non-relativistic versions of AdS/CFT have been a popular venue of recent research. In this talk, I look at the version which can be best motivated as the true non-relativistic limit of the conjecture. The relativistic conformal algebra on the boundary is systematically reduced to what we call the Galilean Conformal Algebra by a process of parametric group contraction. This new algebra is surprising in many aspects, the most intriguing of which is the fact that it can be given an infinite lift in any space-time dimensions. This algebra is also important to non-relativistic hydrodynamics. I look at some interesting features of the two dimensional GCA.The bulk dual of the system is proposed as a novel Newton-Cartan like structure of Anti de-Sitter space-time. The GCA is obtained as the asymptotic symmetries of this novel structure. Several other comments on more recent research would also be made.

Our starting point is an action that describes a general diffeomorphism invariant gauge theory for a group G. The Minkowski background then breaks the gauge group by selecting in it a preferred gravitational SU(2) subgroup. We expand the action around this background and find the spectrum of linearized theory to consist of the usual gravitons plus Yang-Mills fields charged under the centralizer of the SU(2) in G. In addition, there is a set of Higgs fields that are charged both under the gravitational and Yang-Mills subgroups.

Among the spinning string solutions that have proved useful in testing the AdS/CFT correspondence are the giant magnons, which when attached to a giant graviton create a boundary giant magnon. We will discuss the boundary giant magnons on R x S^2 from three different perspectives: as string solutions, as their Pohlmeyer reduced versions in sine-Gordon theory and as BIon spikes of a D3-brane giant graviton.