This series consists of talks in the area of Superstring Theory.
The tt* equations define a flat connection on the moduli spaces of 2d, N=2 quantum field theories. For conformal theories with c=3d, which can be realized as nonlinear sigma models into Calabi-Yau d-folds, this flat connection is equivalent to special geometry for threefolds and to its analogs in other dimensions. I will show that the non-holomorphic content of the tt* equations in the cases d=1,2,3 is captured in terms of finitely many generators of special functions, which close under derivatives.
In this talk, I will prove the Landau-Ginzburg mirror symmetry conjecture for general quasi-homogenous singularities, i.e., the FJRW theory (LG A-model) of such polynomials is equivalent to the Saito-Givental theory (LG B-model) of the mirror polynomial. This is joint work with Weiqiang He, Rachel Webb and Yefeng Shen.
The Ryu-Takayanagi formula relates the entanglement entropy in a conformal field theory to the area of a minimal surface in its holographic dual. I will show that this relation can be inverted to reconstruct the bulk stress-energy tensor near the boundary of the bulk spacetime, from the entanglement on the boundary. I will also show that the positivity and monotonicity of the relative entropy for small spherical domains between the reduced density matrices of an excited state and of the ground state of the CFT, translate to energy conditions in the bulk.
The Truncated Conformal Space Approach (TCSA) is a method that allows for controlled calculations in strongly coupled quantum field theories. It can be used whenever a theory is conformally invariant at short distances, and allows infrared quantities to be calculated in terms of the CFT data of this UV theory.
As an example, I will discuss how the TCSA applies to phi^4 theory in D dimensions and I will show that the method reliably reproduces several nonperturbative phenomena.
> I talk about a method to determine the anomaly polynomials of genera 6d N=(2,0) and N=(1,0) SCFTs, in terms of the anomaly matching on their tensor branches. This method is almost purely field theoretical, and can be applied to all known 6d SCFTs. Green-Schwarz mechanism plays the crucial role.
In this talk I will present some results of an upcoming paper where we study four-dimensional N=2 superconformal field theories using the conformal bootstrap.
We focus on two different four-point functions, involving either the superconformal primary of the flavor current multiplet or the one of the chiral multiplet.
Numerical analysis of the crossing equations yields lower bounds on the allowed central charges, and upper bounds on the dimensions of unprotected operators (for unitary theories).
Renormalized perturbation theory for QFTs typically produces divergent series, even if the coupling constant is small, because the series coefficients grow factorially at high order. A natural, but historically difficult, challenge has been how to make sense of the asymptotic nature of perturbative series. In what sense do such series capture the physics of a QFT, even for weak coupling?
I will talk about 4d N=2 gauge theories with a co-dimension-two full surface operator, which exhibit a fascinating interplay of supersymmetric gauge theories, equivariant Gromov-Witten theory and geometric representation theory. For pure Yang-Mills and N=2* theory, a full surface operator can be described as the 4d gauge theory coupled to a 2d N=(2,2) gauge theory. By supersymmetric localizations, we present the exact partition functions of both 4d and 2d theories which satisfy integrable equations.