Erratum to: Exact summation of leading logs around $$ T\overline{T} $$ deformation of O(N + 1)-symmetric 2D QFTs

A correction to this paper has been published: https://doi.org/10.1007/JHEP05(2021)266

Fishnet four-point integrals: integrable representations and thermodynamic limits

We consider four-point integrals arising in the planar limit of the conformal “fishnet” theory in four dimensions. They define a two-parameter family of higher-loop Feynman integrals, which extend the series of ladder integrals and were argued, based on integrability and analyticity, to admit matrix-model-like integral and determinantal representations. In this paper, we prove the equivalence of all these representations using exact summation and integration techniques. We then analyze the large-order behaviour, corresponding to the thermodynamic limit of a large fishnet graph. The saddle-point equations are found to match known two-cut singular equations arising in matrix models, enabling us to obtain a concise parametric expression for the free-energy density in terms of complete elliptic integrals. Interestingly, the latter depends non-trivially on the fishnet aspect ratio and differs from a scaling formula due to Zamolodchikov for large periodic fishnets, suggesting a strong sensitivity to the boundary conditions. We also find an intriguing connection between the saddle-point equation and the equation describing the Frolov-Tseytlin spinning string in AdS3 × S1, in a generalized scaling combining the thermodynamic and short-distance limits.

Exact summation of leading logs around $$ T\overline{T} $$ deformation of O(N + 1)-symmetric 2D QFTs

We consider a general (beyond $$ T\overline{T} $$ T T ¯ ) deformation of the 2D O(N + 1) σ-model by the irrelevant dimension-four operators. The theory deformed in this most general way is not integrable, and the S-matrix loses its factorization properties. We perform the all-order summation of the leading infrared logs for the 2 → 2 scattering amplitude and provide the exact result for the 2 → 2 S-matrix in the leading logarithmic approximation. These results can provide us with new insights into the properties of the theories deformed by irrelevant operators more general than the $$ T\overline{T} $$ T T ¯ deformation.

Effective free-fermionic form factors and the XY spin chain

We introduce effective form factors for one-dimensional lattice fermions with arbitrary phase shifts. We study tau functions defined as series of these form factors. On the one hand we perform the exact summation and present tau functions as Fredholm determinants in the thermodynamic limit. On the other hand simple expressions of form factors allow us to present the corresponding series as integrals of elementary functions. Using this approach we re-derive the asymptotics of static correlation functions of the XY quantum chain at finite temperature.

Modification of relativistic beam fields under the influence of external conducting and ferromagnetic flat boundaries

We derive analytical expressions for external fields of a relativistic bunch of charged particles with a circular and an elliptical cross section under different boundary conditions and interaction of the fields with an accelerator structural elements. The particle density in the bunch is assumed to be uniform as well as non-uniform. At distances far apart from the bunch, in free space the field reduces to the relativistic modified Coulomb form for a pointlike charge and at small distances the expressions reproduce the external fields of a continuous beam. In an ultra-relativistic limit the longitudinal components of the internal and external electric fields of the bunch are strongly suppressed by the Lorentz factor. If the bunch is surrounded by conducting surfaces, the bunch self-fields are modified. Image fields generated by a bunch between two parallel conducting plates are studied in detail. Exact summation of the electric, $E_y$, and magnetic, $B_x$, image field components allows the infinite series to be represented in terms of elementary trigonometric functions. The new expressions for modified fields are applied to study image forces acting on the bunch constituents and the bunch as a whole. The coherent and incoherent tune shifts for an arbitrary bunch displacement from the midplane are calculated in the framework of an improved linear theory, for both infinite and finite parallel flat surfaces. Moreover, the developed method allows us to generalize the Laslett image coefficients $\epsilon_1$, $\epsilon_2$, $\xi_1$, $\xi_2$ to the case of an arbitrary bunch offset and reveal relationships between these coefficients. Appendix C provides a brief historical background of the development of the method of electrical images.

Dual simulation of the massless lattice Schwinger model with topological term and non-zero chemical potential

We discuss simulation strategies for the massless lattice Schwinger model with a topological term and finite chemical potential. The simulation is done in a dual representation where the complex action problem is solved and the partition function is a sum over fermion loops, fermion dimers and plaquette-occupation numbers. We explore strategies to update the fermion loops coupled to the gauge degrees of freedom and check our results with conventional simulations (without topological term and at zero chemical potential), as well as with exact summation on small volumes. Some physical implications of the results are discussed.

Parallel Online Exact Summation of Floating-point Numbers by Applying MapReduce of Java8

Java8 introduced the notion of streams that is a new data structure and supports multi-core processors. When the sum method is called for a stream of floating-point numbers, the summation is calculated at high-speed by applying MapReduce, which distributes computations to cores. However, since floating-point calculation causes an error, simple adaptation of this method cannot determine the result uniquely. Then, in this study, the authors develop a summation program that can be applied to a stream with MapReduce. Their method can calculate at high-speed with keeping correctly rounded.

Admissibility of weak solutions for the compressible Euler equations, n ≥ 2

This paper compares three popular notions of admissibility for weak solutions of the compressible isentropic Euler equations of gas dynamics: (i) the viscosity criterion, (ii) the entropy inequality (the thermodynamically admissible isentropic solutions), and (iii) the viscosity–capillarity criterion. An exact summation of the Chapman–Enskog expansion for Grad’s moment system suggests that it is the third criterion that is representing the kinetic theory of gases. This, in turn, may shed some light on the ability to recover weak solutions of the Euler equations via a hydrodynamic limit.