The moduli space of Supersymmetric gauge theories with 8 supercharges has a rich structure of symplectic singularities associated with degenerations in which additional massless states arise. These are neatly arranged into phase diagrams that encode the different sets of massless states, with information on the moduli that are needed to be tuned in order to move from one phase to another. We will present results from studies of families of quivers, including those on the affine grassmanian of finite dimensional Lie algebras. ; part of the London TQFT Journal Club (please register at https://london-tqft.vercel.app)

This is the live session included as part of the LonTI lecture on Branes and the moduli space of instantons. Please register at https://lonti.weebly.com/registration.html to receive joining instructions for this live session which will be held via Zoom. Instantons, or solutions to the self dual Yang Mills (SDYM) equations are well known solutions, introduced in the mid 70s and played a role in a host of applications in QFT and String Theory. This talk will show a simple brane construction which allows the computation of the moduli space of solutions to the SDYM equations, introduce the student to the world of quivers, and demonstrate simple computations which allow evaluations of these moduli spaces. ​

The first recorded lecture of the London Theory Institute for PhD Students. Link to recording and problems (to be solved in live Zoom session next Monday) as well as registration details at https://lonti.weebly.com/ and https://youtu.be/CGDNipeuVEs Instantons, or solutions to the self dual Yang Mills (SDYM) equations are well known solutions, introduced in the mid 70s and played a role in a host of applications in QFT and String Theory. This talk will show a simple brane construction which allows the computation of the moduli space of solutions to the SDYM equations, introduce the student to the world of quivers, and demonstrate simple computations which allow evaluations of these moduli spaces.

Instantons appear in many problems of theoretical physics. Quiver gauge theories are a rising subject due to its natural emergence in perturbative open string theories. The talk will discuss features of these two topics and how one can use quiver gauge theories to solve the long standing problem of finding the moduli space of k G instantons on C^2, where G is any simple gauge group, including the non-simply laced cases.

This talk will cover two different applications in the study of Hilbert Series. One is in the text book problem of the massive spectrum of the perturbative string in 10 dimensions. We will write the well known partition function in a new form which is covariant under the little group for massive representations. A second application is in the study of flavor invariants in the standard model. We will compute and count all possible invariants which can be constructed from various mass matrices. These two applications are examples of a larger program in which one can use Hilbert series for a collection of problems in physics. .. (Room EB1 is on the lower ground floor of the Queens' building, which is just in front of the Physics building. It's signed as number 16 on the map http://www.qmul.ac.uk/docs/about/26065.pdf The most convenient entrance is on the east side (again just in front of the Physics building): you go down the stairs to the LG floor and then the room is on your right.)

Brane Tilings give a large class of SCFT's in 3+1 and 2+1 dimensions. In this talk I will discuss several attempts to classify all such models. Special attention will be devoted to the class of Abelian orbifolds of C3 and of C4. Statistical properties of these models can be derived using some techniques in crystallography and in number theory.

Brane Tilings are known to describe the largest known class of SCFT's in 3+1 dimensions. There is a well established formalism to find AdS_5 x SE_5 duals to these SCFT's and to compare results on both sides. This talk extends this formalism to 2+1 dimensional SCFT's, living on the world volume of M2 branes, which are dual to AdS_4 x SE_7 backgrounds of M theory. The SCFT's are quiver gauge theories with 4 supercharges (N=2 in 2+1 dimensions) and Chern Simons (CS) couplings. They admit a moduli space of vacuum configurations which is a CY4 cone over SE_7. The talk will go over the formalism and look at several examples in detail. The computation of scaling dimensions will be mentioned and relations to regular toric Fano 3-folds if time permits.