Triangle Seminars

Abstract:
In this series of 4 or 5 2-hour lectures, I'll describe some of the powerful exact results that one can achieve in supersymmetric theories. The topics will be as follows:

Lecture 1: Non-Renormalization Theorems
Lecture 2: Classical and Quantum Moduli Spaces
Lecture 3: Superconformal Field Theories and Seiberg Duality
Lecture 4: Central Charges, a-maximization, and the a-theorem
Lecture 5 (if it happens): Brane Tilings and Dimers

Abstract:
The algebras of higher spin symmetries in conformal field theories in four and six dimensions are not unique and have a richer structure due to the existence of infinite short multiplets besides the usual scalar and spinor. We will focus on recent results that show there exists a one parameter family (continuous of d=4 and discrete for d=6) of higher spin algebras and superalgebras, and give an explicit unitary representation for these algebras using quasiconformal methods. We will also discuss the implications of these results for the AdS5/CFT4 and AdS7/CFT6 higher spin holography.

Abstract:
In this series of 4-5 2-hour lectures, I'll describe some of the powerful exact results that one can achieve in supersymmetric theories. The topics will be as follows:

Lecture 1: Non-Renormalization Theorems
Lecture 2: Classical and Quantum Moduli Spaces
Lecture 3: Superconformal Field Theories and Seiberg Duality
Lecture 4: Central Charges, a-maximization, and the a-theorem
Lecture 5 (if it happens): Brane Tilings and Dimers

Abstract:
CFTs at large central charge display some universal features which can be inferred from holography. Using these as a guide one can obtain some necessary conditions for a given CFT to admit a classical gravity dual. I will describe attempts to construct a large class of CFTs satisfying these conditions exploiting some technology of permutation orbifolds. Time permitting I will also outline some tests for the sufficiency of these conditions.

Abstract:
I will present this very recently proposed geometric object, conjectured to give the N=4 SYM scattering amplitudes at all orders, and illustrate the techniques used to fully explore its structure. In so doing I will give firm nontrivial evidence to the amplituhedron conjecture.

Abstract:
The algebras of higher spin symmetries in conformal field theories in four and six dimensions are not unique and have a richer structure due to the existence of infinite short multiplets besides the usual scalar and spinor. We will focus on recent results that show there exists a one parameter family (continuous of d=4 and discrete for d=6) of higher spin algebras and superalgebras, and give an explicit unitary representation for these algebras using quasiconformal methods. We will also discuss the implications of these results for the AdS5/CFT4 and AdS7/CFT6 higher spin holography.

Abstract:
Taking inspiration from lattice QCD data, we argue that a finite
non-perturbative mass contribution for quarks is generated as another consequence of
the dynamical phenomenon of spontaneous chiral symmetry breaking, which is in turn
triggered by the explicitly breaking of chiral symmetry induced by the critical
Wilson term in the action. In pure lattice QCD this mass term cannot be
separated from the unavoidably associated linearly divergent contribution.
However, if QCD is enlarged to a theory where also a scalar field is present,
coupled to a doublet of SU(2) fermions via a Yukawa and a Wilson-like term,
then in the phase where the scalar field takes a non-vanishing expectation
value, a dynamically generated and "naturally" light fermion mass (numerically
unrelated to the expectation value of the scalar field) is conjectured to
emerge at a critical value of the Yukawa coupling where the symmetry of the
model is maximally enhanced. Masses dynamically generated in this way display a
natural hierarchy according to which the stronger is the strongest of the
interactions the fermion is subjected to the larger is its mass.

Abstract:
In recent years there is a growing interest in unconventional string backgrounds with non-geometric fluxes. The latter often appear after
repeated T-dualities on known backgrounds. However, a very interesting question regards whether these fluxes can coexist in generalized geometries
without a geometric dual. In this talk we address this question and we show that in principle there exist such geometries where all types of fluxes coexist.
Our strategy consists in using generalized geometry and in particular Dirac structures, which are subbundles of the generalized tangent bundle where the
Courant bracket is associative and field strengths transform tensorially. We study the mathematical description of fluxes on Dirac structures and then combine the
latter into Courant algebroids that describe multi-flux geometries. Furthermore we discuss the sources of non-geometric fluxes, which are heavy extended objects
known as exotic branes. These branes exhibit a wide range of world volume dimensions, tension scalings and monodromy properties, and we argue that they couple to
certain mixed symmetry tensors, which are exotic magnetic duals of the supergravity background fields.