My Research

In general, computing loop-level scattering amplitudes of (non-supersymmetric) QFTs is hard. In particular going beyond two-loop computations in ordinary QCD has proven difficult. It turns out that we can obtain certain scattering amplitudes (probability amplitudes corresponding to particle interactions during scattering) in QCD (coupled to either special matter content or an additional field called the 'axion') by instead considering a very special 4d theory (3 spatial + 1 temporal dimensions) which can be mapped to 6 dimensions (to something called Twistor Space). 

This approach involves the ordered product expansion (representation of what happens as local operators approach each other; also known as OPE) of towers of operators which couple to the fields of the 6d theory. These OPEs are written as a perturbative series with parameter ℏ (the power of ℏ corresponds to the loop-level of the contribution). Having obtained the all-loop OPEs, we can obtain all-loop results for these scattering amplitudes.

In this paper, I determined the one-loop contributions to the OPEs by explicitly performing the 6d Feynman diagram integrals (in position space). 

This is a continuation of work done by both authors.

The set up is the same as the paper above with the main difference coming from the fact that we now couple our theory to:

Using arguments of symmetry, we determine the contributing 6d Feynman diagrams at every loop-level. With this information we work out a general form of the all-loop OPEs  in terms of unknown coefficients. Lastly, we solve for these unknown coefficients by enforcing 'associativity' of the OPEs order-by-order in ℏ (loop-level). 

We also briefly go over how we can perform the same steps to obtain the all-loop order OPEs in the case of a special theory which corresponds to graviton amplitudes.

In this work, we use many of the methods used in the two papers above but instead we focus on twisted holography for AdS3 × S3 × X with X = T4 , K3, with a particular focus on K3. 

We describe the twist of supergravity, identify the corresponding (generalization of) BCOV theory, and enumerate twisted supergravity states. We use this knowledge, and the technique of Koszul duality, to obtain the N → ∞, or planar, limit of the chiral algebra of the dual CFT. 

The resulting symmetries are strong enough to fix planar 2 and 3-point functions in the twisted theory or, equivalently, in a 1/4-BPS subsector of the original duality. 

This technique can in principle be used to compute corrections to the chiral algebra perturbatively in 1/N