I will give a broad overview of techniques in resurgent analysis and transseries, as they apply in string theory and matrix models (and with some focus on Painlevé type equations).
We will motivate and introduce the study of conformal defects in superconformal field theories (SCFTs). We will show how symmetries constrain the anomaly coefficients of BPS defects. In the case of N=(2,2) surface defects in four-dimensional N=2 SCFTs these anomaly coefficients can be computed by studying a protected subsector captured by a vertex operator algebra, or two-dimensional chiral algebra.
I will review recent and on-going work concerning applications of resurgence within the realm of minimal-string and JT quantum gravities in 2d.
Integrability techniques have played a major role in the study the AdS/CFT correspondence, providing an accurate description of different string theoretic observables beyond the weak or strong coupling perturbation theory. However, the case of string on certain AdS_3 backgrounds provided new challenges in the form of massless excitations. Difficulties in incorporating these into the integrable description have led to disagreements concerning the energy of massive physical states.
In general integrable theories, massless and massive sectors can generally be treated separately. We know this cannot be the case in AdS_3, but a full TBA description of the interaction between the sectors is yet to be found. Surprisingly, such a description can found in a family of integrable field theories — homogeneous sine-Gordon models. Here, one can take a double scaling limit of the adjustable parameters and zoom into a regime described by a TBA where the massless sector does not decouple and contributes to the energy of massive particles at the same order as for which the Bethe ansatz would suffice in a massive theory.
Integrability techniques have played a major role in the study the AdS/CFT correspondence, providing an accurate description of different string theoretic observables beyond the weak or strong coupling perturbation theory. However, the case of string on certain AdS3 backgrounds provided new challenges in the form of massless excitations. Difficulties in incorporating these into the integrable description have led to disagreements concerning the energy of massive physical states.
In general integrable theories, massless and massive sectors can generally be treated separately. We know this cannot be the case in AdS3, but a full TBA description of the interaction between the sectors is yet to be found. Surprisingly, such a description can found in a family of integrable field theories — homogeneous sine-Gordon models. Here, one can take a double scaling limit of the adjustable parameters and zoom into a regime described by a TBA where the massless sector does not decouple and contributes to the energy of massive particles at the same order as for which the Bethe ansatz would suffice in a massive theory.
We study BPS surface defects in 4d superconformal field theories and show how symmetries constrain their anomaly coefficients. Focusing on N=(2,2) surface defects we review the protected subsector captured by a two-dimensional chiral algebra. We study the properties of the defect in this subsector and discuss how to compute the aforementioned anomaly coefficients.
We study BPS surface defects in 4d superconformal field theories and show how symmetries constrain their anomaly coefficients. Focusing on N=(2,2) surface defects we review the protected subsector captured by a two-dimensional chiral algebra. We study the properties of the defect in this subsector and discuss how to compute the aforementioned anomaly coefficients.
We will give introductions to the topics of Kahler geometry, geometry on the space of Kahler metrics and geometric quantization. We will then see how the 3 topics interact strongly with each other and will describe some examples. Namely we will describe how quantization in so-called real polarizations can sometimes be related to the (easier to define) quantization in Kahler polarizations. Geodesics for a natural metric structure on the space of Kahler metrics play a central role in this relation.
We study symmetry constraints on BPS surface defects in four-dimensional superconformal field theories, showing how supersymmetry imposes relations on anomaly coefficients. Turning to dynamics, we analyze a protected subsector of N=(2,2) surface defects that is captured by a two-dimensional chiral algebra. We discuss how to compute observables of interacting defects from the chiral algebra, including the aforementioned anomaly coefficients.
One can obtain a two-dimensional chiral algebra, or vertex operator algebra, as a protected subsector of any four-dimensional N>1 SCFT. In these lectures we will review the construction of the chiral algebra, and the basic properties that follow from its four-dimensional origin. We will also explore some of the consequences for four-dimensional physics.
Following a recent revival of interest in 2-dimensional gravity due to the holographic properties of Jackiw-Teitelboim gravity, we investigate the non-perturbative properties of such models using the tools offered by Resurgence. This leads to non-trivial results concerning the asymptotics of Weil-Petersson volumes and the instanton contributions to 2-dimensional topological gravity.
We study symmetry constraints on BPS surface defects in four-dimensional superconformal field theories, showing how supersymmetry imposes relations on anomaly coefficients. Turning to dynamics, we analyze a protected subsector of N=(2,2) surface defects that is captured by a two-dimensional chiral algebra. We discuss how to compute observables of interacting defects from the chiral algebra, including the aforementioned anomaly coefficients.