The systematic construction of string theory duals for (perturbative) field theories, such as Quantum Chromodynamics (QCD), would be a major advance in the quest to access non-perturbative physics. Symmetric orbifold theories in 2-dimensional conformal field theories (CFTs) provide a promising stage to explore new ideas for such a perturbative holography. While they can be controlled with the rich toolbox of 2D CFTs they do share some basic features with their higher dimensional gauge theory cousins. In my talk, I will show the engineering of dual string backgrounds at work in the context of some symmetric product orbifolds. The construction ensures that the amplitudes of the dual string theory inherently reproduce the correlation functions of the two-dimensional CFT, order-by-order in perturbation theory, without requiring explicit computation on either side of the correspondence.

While Feynman integrals and scattering amplitudes are often very difficult to compute directly, their underlying properties point to new approaches. Cuts of diagrams are a tool for their efficient computation, related to unitarity and singularities. I will present definitions and interpretations of cuts, and ways to embed them in new frameworks which can be used to construct the original integrals and amplitudes.

We discuss numerical results from integrability for the Hagedorn temperature in N=4 SYM and ABJM theory at strong coupling and compare them to the Hagedorn temperatures of their string theory duals. From the numerics we conjecture the leading analytic coefficients in the expansion about large 't Hooft coupling. This talk is based on arXiv:2306.09883 and arXiv:2307.02350.

I'll discuss recent results on line and surface defects in the N=4 Super-Yang-Mills (SYM) beyond perturbation theory. In addition to providing new observables in the SYM that capture the gauge theory dynamics in the presence of impurities, these non-perturbative results detect the nontrivial SL(2,Z) structure and provide an exact order parameter for the deconfinement phase transition. Furthermore, via AdS/CFT, they lead to novel predictions for the world-volume action of branes in type IIB string theory at finite string coupling and present a new perspective on the Hawking-Page transition for black holes in AdS.

In this talk, I will discuss the possibility that our universe lies near the boundary of the field space in string theory, including the theoretical challenges and the exciting phenomenological implications. These boundaries share some universal properties imposed by quantum gravity (sometimes promoted to Swampland constraints) that resemble our universe, like weak couplings, approximate global symmetries or small (time-dependent) vacuum energy. However, it remains as an open challenge to get an accelerated cosmology. We study whether the runaway behaviour of stringy scalar potentials towards in finite distance can produce an accelerated expanding cosmology a la quintessence, finding some potential examples in F-theory flux compactifications. I will discuss the caveats of these examples and the comparison to Swampland bounds. Furthermore, a universal feature of these regions is that there is a light infinite tower of states which is correlated to the value of the vacuum energy. I will show how experimental constraints force this tower to correspond to a KK tower (of mass of order neutrino scale) of a single extra mesoscopic dimension of order 10^{-6) m, which we denote as the Dark Dimension.

We know that quantum gravity is expected to violate global symmetries of effective gravity theories. Black holes are expected to play a role in this violation. We discuss computations of gravity amplitudes, mainly involving scattering of spherically symmetric shells, that violate global symmetries. We will review prior work in two dimensions and we will discuss the new features that arise in higher dimensions.

I will review the basic assumptions and spell out the detailed arguments that lead to the bound on the Regge growth of gravitational scattering amplitudes. The minimal extra ingredient compared to the gapped case - in addition to unitarity, analyticity, and crossing - that goes into the derivation is the assumption that scattering at large impact parameters is controlled by known semi-classical physics. I will also discuss bounds on the local growth of scattering amplitudes. Contact your local Triangle organiser or Bogdan Stefanski for Zoom link.

I will discuss how to constrain four-point correlators involving at least one quarter BPS operator in N=4 Super Yang-Mills. I will present what can be learned by using crossing symmetry, chiral algebra, superspace techniques, and the structure of the operator product expansion. Finally, I will show how to make contact with the superconformal bootstrap program. Contact your local Triangle organiser or Bogdan Stefanski for Zoom link.

D-instantons give non-perturbative contribution to string theory amplitudes which can be computed using world-sheet techniques. However the integrals that appear in this computation often have divergences from corners of the moduli spaces which cannot be tamed by the usual procedure of analytic continuation. We show how using insights from string field theory we can extract finite unambiguous results from these apparently divergent integrals. The Zoom link will be sent by your local Triangle seminar organiser or you can contact bogdan.stefanski.1@city.ac.uk

This is the live session included as part of the LonTI lecture on Conformal blocks in two dimensions. Please register at https://lonti.weebly.com/registration.html to receive joining instructions for this live session which will be held via Zoom. D-branes are a remarkable set of soliton-like objects in string theory which have played a critical role in many areas of string theory. Despite being non-perturbative, they can be understood exactly using world-sheet methods through the boundary state formalism. In this lecture, I introduce the notion of a boundary state and show how to use it to extract physical information about D-branes and the open strings that live on them.

This seminar will be held over Zoom. The link will be sent by your local Triangle seminar organiser or you can contact bogdan.stefanski.1@city.ac.uk for link. I will report on some work in progress on type I topological strings on twistor space, and their relationship with integrable but non-supersymmetric field theories in three and four dimensions. This is closely related to recent work of Bittleston and Skinner.

This seminar will be held over Zoom. The link will be sent by your local Triangle seminar organiser or you can contact bogdan.stefanski.1@city.ac.uk for link. We propose machine learning inspired methods for computing numerical Calabi-Yau metrics, and implement them using Tensorflow/Keras. We compare them with previous work, and find that they are far more accurate for manifolds with little or no symmetry. We also discuss issues such as optimization methods, overparameterization and computational complexity. Joint work with Subramanian Lakshminarasimhan and Yidi Qi.

D-branes are a remarkable set of soliton-like objects in string theory which have played a critical role in many areas of string theory. Despite being non-perturbative, they can be understood exactly using world-sheet methods through the boundary state formalism. In this lecture, I introduce the notion of a boundary state and show how to use it to extract physical information about D-branes and the open strings that live on them.

I will discuss the connection between W-algebras, the higher spin generalizations of the Virasoro algebra which are the symmetry algebras in the 2-dimensional conformal field theory, and Tsymbaliuk's affine Yangian. The bridge between these two algebraic structures is the Miura operator which on one hand provides free field representations of W-algebras and on the other hand satisfies the RTT equations with Maulik-Okounkov R-matrix. The associated integrable structure allows one to easily reproduce many well-known results in conformal field theory.

I will discuss FZZT branes and long strings in c=1 string theory, and the dual description of the latter in non-singlet sectors of the matrix quantum mechanics. I will present highly nontrivial evidences for the duality at the level of perturbative scattering amplitudes, and discuss implications on black holes in c=1 string theory and their matrix model duals.