We review infrared properties of scattering amplitudes in gauge theories, with a particular emphasis on planar N = 4 superYang–Mills (SYM) theory. We then discuss a web of dualities that relate amplitudes to seemingly different observablesin planar N = 4 SYM: light-like polygonal Wilson loops, correlation functions of local half-BPS operators, and theirstrong-coupling counterparts in AdS/CFT. We then focus on a recently uncovered duality between scattering amplitudeson the Coulomb branch, in a “pseudo off-shell’’ kinematic regime with small W-boson masses, and correlation functions ofoperators with large R-charge. This Coulomb amplitudes/heavy-correlator duality will be illustrated in detail for the caseof a five-point correlator and the corresponding five-W-boson amplitude evaluated to two loops in the pseudo off-shelllimit. The example provides non-trivial evidence for yet another duality that connects Coulomb-branch amplitudes andheavy correlators in planar N = 4 SYM.

I will discuss flux tubes, or strings, in confining gauge theories focusing on large-N pure Yang-Mills theory. After reviewing briefly the recent progress in understanding the long strings in flat space both form effective field theory and form the lattice,I will discuss the new analytic approach that uses AdS space as an IR regulator. For AdS radius large, compared to the confinement scale, we recover the usual confining string. For small radius gauge theory is perturbative and we find a weakly coupled string-like object held together by the AdS gravitational potential. Power of conformal symmetry allows us to establish a smooth interpolation between the two regimes. Time permitting, I will also mention a connection with AdS/CFT integrability.

We propose a perturbatively exact relation between scattering amplitudes in bosonic theories and vacuum-to-vacuum transition amplitudes in the same theories with vanishingly small source on a singular background. The derivation of this formula is based on the exact version of quantum-mechanical Landau method. Being applied to the amplitudes of n ≫ 1 particle production, it resums the powers of g 2 · n in the perturbative series, where g is a coupling constant, thus describing the double-scaling limit g → 0, g 2 · n =const. In the lowest semiclassical order, it reproduces non-perturbative Rubakov-Son-Tinyakov conjecture. We verify our new relation by explicitly computing transition amplitudes between vacuum and highly excited states of anharmonic oscillator and discuss its application to multiparticle production in the scalar φ4 theory.

We obtain localized field configurations with finite energy in a (2 + 1)-dimensional model with Maxwell and Chern–Simons gauge terms coupled to a massive complex scalar field. These non-topological solitons are characterized by the U (1) frequency and a winding number. Thus, the solutions possess Noether charge and non-trivial angular momentum, which is not quantized in contrast to the topological case. We study the solitons and their integral characteristics numerically and demonstrate that they are kinematically stable. The obtained solutions allow for the thin-wall approximation in some region of frequencies. For each winding number, the Noether charge has a lower bound that coincides with isolated point, where seemingly the non-relativistic conformal symmetry is restored.

We study cosmological correlators in de Sitter quantum gravity in the limit where $G_N \to 0$. This limit is distinct from a non-gravitational QFT because the gravitational constraints still force states and observables to be de Sitter invariant.  We show that, in the presence of a heavy background state, it is possible to construct a separate class of state-dependent relational observables whose values approximate QFT correlators in the vacuum. This illustrates a key contrast in quantum gravity -- between observables that are microscopically simple and observables whose expectation values in an appropriate background state lead to simple QFT-like correlators.

I will introduce non-commutative resolutions of singular Calabi–Yau double covers, to investigate the notion of B-brane on these spaces. The non-commutative geometry is studied via a GLSM description, and B-branes in these GLSMs provide the non-commutative analogues of sheaves on smooth Calabi–Yau manifolds.Computing the central charges of the B-branes,I will show that they are annihilated by the GKZ system of the mirror singular Calabi–Yau, when the latter is known. We show that(i) There always exists a smooth Calabi–Yau complete intersection which satisfies the same GKZ system; (ii) The B-branes on the non-commutative resolution form the invariant sub-category of a certain equivariant category of coherent sheaves on the smooth complete intersection. This is a universal phenomenon, which allows us to find the GKZ system forthe mirror Calabi–Yau, even when the mirror geometry is not known.Based on joint work with Tsung–Ju Lee, Bong Lianand Mauricio Romo.

The six-vertex model is arguably the most famous 2D integrable lattice model. Less known is the fact that the model has a 3D origin. In this talk I will discuss the quantization of the six-vertex model, introduced by Kuniba, Matsuike and Yoneyama in 2022 generalizing earlier work of Bazhanov, Mangazeev and Sergeev. The quantized six-vertex model is a 3D integrable lattice model, which has a remarkable property that commuting layer transfer matrices can be defined not only for square lattices but also on more general "admissible" graphs on a torus. Time permitting, I will also explain how the model is related to dimer models, supersymmetric gauge theories and string theory.

The talk is devoted to the three-loop renormalization of the effective action for a two-dimensional principal chiral field model using the background field method and a cut-off regularization in the coordinate representation. The coefficients of the renormalization constant and the necessary auxiliary vertices are found. Asymptotic expansions for all three-loop diagrams and their dependence on the type of regularization function are also studied.

There are quantities in Chern-Simons theory that can be expressed as rational functions of Vogel’s parameters, which accumulate all the dependency on a gauge group. This phenomenon is called algebraic universality in Vogel’s sense. Among hese quantities are quantum dimensions, Wilson loop averages (knot invariants) and Chern-Simons partition function.Refinement of Chern-Simons theory means introducing additional parameters, and at the level of symmetric functions it is the transition from Schur symmetric functions to Macdonald polynomials. The question is whether algebraic universality is preserved after refinement. Turns out it survives only for simply-laced root systems. We will compare properties of Schur symmetric functions and Macdonald polynomials associated with different root systems, and discuss algebraic universality of Macdonald dimensions, which are the simplest refined quantity.

We propose the explicit construction of fields in orbifolds of products of N = (2, 2) Superconformal minimal models with A-D-E type modular invariants. Such theories have central charge c=9 and arise as a compact sector of Superstring compactification. We use spectral flow twisting of fields by the elements of admissible group G. We obtain the complete set of fields of the orbifold from the mutual locality and other requirements of the conformal bootstrap. The collection of mutually local primary fields is labelled by the elements of dual group G∗. The permutation of G and G* is given by the mirror spectral flow construction of the fields and maps the space of states of the original G orbifold onto the space of states of G∗ orbifold. We show that this transformation is by construction a mirror isomorphism of spaces of states.

We will discuss the construction of a representation of the so(2,5) algebra corresponding to a continuous-spin field in AdS₆. Part I. Geometric Formulation of Casimir Operators. In this part of the talk we will describe the realization of the so(2,5) algebra using the Lie-Lorentz derivative, which unifies AdS6 geometry and spin degrees of freedom. We will derive explicit expressions for the Casimir operators in terms of the covariant derivative and the spin part of the angular momentum operators.

Critical phenomena are quite widespread in the world around us: from the Curie point of the magnets to the merger of liquid and vapour phases. These phenomena are known to be described by the conformal field theory (CFT). It is a field theory of a very special kind, which captures the scale invariance property of the system in question, arising naturally, as the system approaches the critical point. The study of CFTs achieved its greatest success in dimension d = 2, due to the fact that the algebra of conformal symmetries in this case is an infinite-dimensional Virasoro algebra. In d > 2, this is no longer the case; hence, the analytic results for higher-dimensional CFTs are mostly limited to supersymmetric systems, and people have to resort to numerical methods. In a recent paper, Mikhail Kapranov proposed an idea to reclaim a version of this infinite-dimensionality in d > 2 CFT by studying the derived analogue of the Virasoro algebra, which ties together both infinitesimal symmetries and deformations of the conformal structure. To describe it explicitly, he used the ambitwistorspace construction: the space of all null geodesics, encoding the conformal geometry of the original manifold. Concretely,consider the sheaf of holomorphic contact Hamiltonian vector fields on the ambitwistor space of a d-dimensional complex plane. Kapranov’s higher-dimensional Virasoro algebra is a derived functor of the global sections of this sheaf. It is endowed with the structure of a dg-Lie algebra through Dold–Kan/Thom–Sullivan correspondence. I will write this algebra down explicitly in terms of generators and relations in the d = 2 and d = 3 cases, and explain how to find its central extension, which is crucial for physical applications.

Within the AdS/CFT correspondence, computational complexity for reduced density matrices of holographic conformal field theories has been conjectured to be related to certain geometric observables in the dual gravity theory. We studythis conjecture from both the gravity and field theory point of view. Specifically, we consider a measure of complexity associated to the Bures metric on the space of density matrices. We compute this complexity measure for mixed states associated to single intervals in descendant states of the vacuum in 2d CFTs. Moreover, we derive from first principles a geometric observable dual to the Bures metric which is localized in the entanglement wedge of the AdS spacetime associated to the quantum circuit on the boundary. Finally, we compare the Bures metric complexity measure with holographic subregion complexity within the «complexity=volume» paradigm for perturbatively small transformations of the vacuum.While there is no exact agreement between these two quantities, we find striking similarities as we vary the target state and interval size, suggesting that these quantities are closely related.

In this talk, I will discuss two types of inelastic scattering processes of a single quantum of radiation off a domain wall string in a general (2+1)-dimensional scalar model. These processes involve the excitation and de-excitation of the wall’s internal shape mode and are referred to as Stokes and anti-Stokes scattering. We calculate the probability densities for these processes to first order in quantum field theory, as a function of incoming momenta and angles. Our results are given as finite-dimensional integrals of normal modes and elementary functions, and numerical results are presented in the particular case of the φ4 double-well model.

Celestial CFT_d is the putative dual of quantum gravity in asymptotically flat d+2 dimensional space time. We argue that a class of Celestial CFT_d can be engineered via AdS_{d+1}-CFT_d correspondence. Our argument is based on the observation that if we have a non-conformal theory of gravity on EAdS_{d+1}$  then the near boundary scaling limit of such a theory is dual to boundary Celestial CFT_d with only SO(d+1,1) Lorentz invariance. We study more such examples: the near boundary scaling limit of the bosonic string theory on Euclidean AdS_3 and the conformal gravity theory on EAdS_{d+1}

We propose a formulation of the N=2 hypermultiplet in harmonic superspace within the framework of the unfolded dynamics approach of higher-spin theory. Using the properties of this approach, we manifestly describe the symmetries of the model and their realizations in various background spaces.

We present new approaches to constructing supersymmetric solutions in 5d gauged supergravity. Firstly, a geometric approach involves identifying new classes of Kahler spaces, which are key building blocks of supersymmetric 5d solutions.These new classes possess hidden symmetries that simplify supersymmetry conditions, and thus allow for deeper analysis.Secondly, we explore the space of static supersymmetric solutions and find several families of Euclidean solutions that may have interpretation on the CFT side.

The continuum formulation of noncritical string theory (super string) is equivalent to two-dimensional quantum gravity coupled to conformal matter, giving rise to Liouville (super Liouville) gravity as the effective description of the dynamics of the metric. In this talk, we will discuss the construction of the so-called correlation numbers in N=1 super minimal Liouville gravity. In particular, we construct the fundamental physical fields in the Ramond sector and compute the three-point correlation number involving two physical fields in the Ramond sector and one in the NS sector. Furthermore, we establish the relation between Ramond physical fields and the elements of the ground ring. Using the higher equations of motion of super Liouville theory, this relation leads to a new representation of the Ramond physical fields. This formulation enables adirect analytic computation of correlation numbers involving Ramond field insertions. As an application, we demonstrate the method in the simplest case of a three-point correlation function. The talk will be based on work arxiv:2505.23122

AKSZ construction is a powerful tool for studying and classifying topological field theories which involves the language of graded geometry. The generalization of the non-Lagrangian version of AKSZ sigma-models to generic local gauge theories is known under the name of gauge PDEs. Gauge PDEs are supergeometrical objects that encode the BV description of local non-Lagrangian gauge theories. Just like AKSZ sigma-models, gPDEs behave well when restricted to submanifolds, which makes them useful in the study of gauge theories on manifolds with boundaries. However, gPDEs are infinite-dimensional unless the underlying system is a PDE of finite type or a topological theory. Weak gauge PDE is a finite-dimensional analogue of a gPDE in which the BRST-differential Q is nilpotent modulo certain integrable Q-invariant distribution.These finite-dimensional objects can be considered as a far-reaching generalization of the AKSZ construction