For each admissible group, we explicitly construct a special set of primary fields of the corresponding orbifold model using the spectral flow winding and the requirement of mutual locality. Then we show that the OPE of the constructed fields is closed. We also show that the mutual locality ensures the modular invariance of the partition function of the resulting orbifold. Using various examples of orbifolds, we construct chiral and antichiral rings and show that they coincide with the cohomology groups of mutually mirrored CY-manifolds.

We study the density of states (DoS) ν(E) in a normal-metallic (N) film contacted by a bulk superconductor (S). We assume that the system is diffusive and the SN interface is transparent. In the limit of thin N layer (compared to the coherence length), we analytically find three different types of the DoS peculiarity at energy equal to the bulk superconducting order parameter Δ₀. (i) In the absence of the inverse proximity effect, the peculiarity has the check-mark form with ν(Δ₀)=0 as long as the thickness of the N layer is smaller than a critical value. (ii) When the inverse proximity effect comes into play, the check-mark is immediately elevated so that ν(Δ₀)>0. (iii) Upon further increasing of the inverse proximity effect, ν(E) gradually evolves to the vertical peculiarity (with an infinite-derivative inflection point at E=Δ₀). This crossover is controlled by a materials-matching parameter which depends on the relative degree of disorder in the S and N materials.
arXiv:2205.06171

We study of integrable structures in superconformal field theory and more general coset CFT’s related to the affine Yangian Y(\hat{\mathfrak{gl}}gl^​(2)). We derive the relation between the RLL and current realizations and prove Bethe anzatz equations for the spectrum of Integrals of Motion.

We study regularization scheme dependence of β-function for sigma models with two-dimensional target space. Working within four-loop approximation, we conjecture the scheme in which the β-function retains only two tensor structures up to certain terms containing ζ_{3}3​. Using this scheme, we provide explicit solutions to RG flow equation corresponding to Yang-Baxter- and λ-deformed SU(2)/U(l) sigma models, for which these terms disappear.

Folding transformation of the Painleve equations is an algebraic (of degree greater than 1) transformation between solutions of different equations. In 2005 Tsuda, Okamoto and Sakai classified folding transformations of differential Painleve equations. These transformations are in correspondence with automorphisms of affine Dynkin diagrams. We give a complete classification of folding transformations of the q-difference Painleve equations, these transformations are in correspondence with certain subdiagrams of the affine Dynkin diagrams (possibly with automorphism). The method is based on Sakai's approach to Painleve equations through rational surfaces.
Based on joint work with A. Shchechkin [arXiv:2110.15320]

Evolution of wavefront geometry during propagation and attenuation of initially planar shock waves generated by femtosecond laser pulses in aluminum is studied. We demonstrate that three stages of shock front inflection take place in consistent hydrodynamics and molecular dynamics simulations. During the first stage, the distance traveled by a near-planar wave DSW ≲ RL is smaller than the radius of heated laser spot RL. Wave attenuation is associated with one-dimensional plane (1D) rarefaction wave coming from the free surface. Such rarefaction wave shapes the shock wave to a 1D triangular pressure profile along direction normal to target surface with a shock front followed by an unloading tail. The second transitional stage starts after propagation of DSW ∼ RL, at which the unloading lateral waves begin to arrive to a symmetry axis of flow and initiate inflection of the initially planar shock front. Next at the third stage, the wavefront geometry is finally rounded and rapid attenuation of shock pressure begins at DSW ≳ RL. It is shown that such divergent shock wave cannot generate plastic deformations in aluminum shortly after propagation of DSW ∼ RL. Thus, we may estimate the maximal peening depth as a radius of focal spot, which sets an upper limit for the laser shock peening. The cessation of plastic deformation is caused by the fall of the shockwave amplitude below the elastic limit. In this case, the elastic-plastic wave transitions to a purely elastic mode of propagation. For large-sized light spots, this transition ends in the 1D mode of propagation.

We propose a string theory construction for the system of two heavy quarks and two light antiquarks. The potential of the system is a function of separation between the quarks. We define a critical separation distance below which the system can be thought of mainly as a compact tetraquark. The results show the universality of the string tension and factorization at small separations expected from heavy quark-diquark symmetry. Our estimate of the screening length is in the range of lattice QCD. We also make a comparison with the potential of the $QQq$ system. The potentials look very similar at small quark separations but at larger separations they differ. The reason for this is that the flattening of the potentials happens at two well-separated scales as follows from the two different mechanisms: string breaking by light quarks for $QQq$ and string junction annihilation for $QQ\bar q\bar q$. Moreover, a similar construction can also be applied to the $\bar Q\bar Q qq$ system.