Testing a new method for scattering in finite volume in the $$\phi ^4$$ theory

We test an alternative proposal by Bruno and Hansen (J High Energy Phys 2021(6), 10.1007/JHEP06(2021)043, 2021) to extract the scattering length from lattice simulations in a finite volume. For this, we use a scalar $$\phi ^4$$ ϕ 4 theory with two mass nondegenerate particles and explore various strategies to implement this new method. We find that the results are comparable to those obtained from the Lüscher method, with somewhat smaller statistical uncertainties at larger volumes.

Harmonic Analysis in d-Dimensional Superconformal Field Theory

Superconformal blocks and crossing symmetry equations are among central ingredients in any superconformal field theory. We review the approach to these objects rooted in harmonic analysis on the superconformal group that was put forward in [J. High Energy Phys. 2020 (2020), no. 1, 159, 40 pages, arXiv:1904.04852] and [J. High Energy Phys. 2020 (2020), no. 10, 147, 44 pages, arXiv:2005.13547]. After lifting conformal four-point functions to functions on the superconformal group, we explain how to obtain compact expressions for crossing constraints and Casimir equations. The later allow to write superconformal blocks as finite sums of spinning bosonic blocks.

More on the infrared renormalon in SU (N) QCD(adj.) on $\mathbb{R}^3\times S^1$

We present additional observations to previous studies on the infrared (IR) renormalon in $SU(N)$ QCD(adj.), the $SU(N)$ gauge theory with $n_W$-flavor adjoint Weyl fermions on $\mathbb{R}^3\times S^1$ with the $\mathbb{Z}_N$ twisted boundary condition. First, we show that, for arbitrary finite $N$, a logarithmic factor in the vacuum polarization of the “photon” (the gauge boson associated with the Cartan generators of $SU(N)$) disappears under the $S^1$ compactification. Since the IR renormalon is attributed to the presence of this logarithmic factor, it is concluded that there is no IR renormalon in this system with finite $N$. This result generalizes the observation made by Anber and Sulejmanpasic [J. High Energy Phys. 1501, 139 (2015)] for $N=2$ and $3$ to arbitrary finite $N$. Next, we point out that, although renormalon ambiguities do not appear through the Borel procedure in this system, an ambiguity appears in an alternative resummation procedure in which a resummed quantity is given by a momentum integration where the inverse of the vacuum polarization is included as the integrand. Such an ambiguity is caused by a simple zero at non-zero momentum of the vacuum polarization. Under the decompactification $R\to\infty$, where $R$ is the radius of the $S^1$, this ambiguity in the momentum integration smoothly reduces to the IR renormalon ambiguity in $\mathbb{R}^4$. We term this ambiguity in the momentum integration “renormalon precursor”. The emergence of the IR renormalon ambiguity in $\mathbb{R}^4$ under the decompactification can be naturally understood with this notion.

Non-compact superconformal field theory and mock modular forms

One of interesting issues in two-dimensional superconformal field theories is the existence of anomalous modular transformation properties appearing in some non-compact superconformal models, corresponding to the “mock modularity” in mathematical literature. I review a series of my studies on this issue in collaboration with T. Eguchi, mainly focusing on T. Eguchi and Y. Sugawara, J. High Energy Phys. 1103, 107 (2011); J. High Energy Phys. 1411, 156 (2014); and Prog. Theor. Exp. Phys. 2016, 063B02 (2016).

The q-linked complex Minkowski space, its real forms and deformed isometry groups

We establish duality between real forms of the quantum deformation of the four-dimensional orthogonal group studied by Fioresi et al. [Quantum Klein space and superspace, preprint (2017), arXiv:1705.01755] and the classification work made by Borowiec et al. [Basic quantizations of [Formula: see text] Euclidean, Lorentz, Kleinian and quaternionic [Formula: see text] symmetries, J. High Energy Phys. 1711 (2017) 187]. Classically, these real forms are the isometry groups of [Formula: see text] equipped with Euclidean, Kleinian or Lorentzian metric. A general deformation, named [Formula: see text]-linked, of each of these spaces is then constructed, together with the coaction of the corresponding isometry group.

Colored knot polynomials: HOMFLY in representation [2, 1]

This paper starts a systematic description of colored knot polynomials, beginning from the first non-(anti)symmetric representation [Formula: see text]. The project involves several steps: (i) parametrization of big families of knots á la [A. Mironov and A. Morozov, arXiv:1506.00339], (ii) evaluating Racah/mixing matrices for various numbers of strands in various representations á la [A. Mironov, A. Morozov and An. Morozov, J. High Energy Phys. 03, 034 (2012), arXiv:1112.2654], (iii) tabulating and collecting the results at http://www.knotebook.org . In this paper, we discuss only the representation [Formula: see text] and construct all necessary ingredients that allow one to evaluate knot/links represented by three-strand closed parallel braids with inserted double-fat fingers. In particular, it is used to evaluate knots from a 7-parametric family. This family contains over 80% of knots with up to 10 intersections, but does not include mutants.

Evaluating the six-point remainder function near the collinear limit

The simplicity of maximally supersymmetric Yang–Mills theory makes it an ideal theoretical laboratory for developing computational tools, which eventually find their way to QCD applications. In this contribution, we continue the investigation of a recent proposal by Basso, Sever and Vieira, for the nonperturbative description of its planar scattering amplitudes, as an expansion around collinear kinematics. The method of G. Papathanasiou, J. High Energy Phys.1311, 150 (2013), arXiv:1310.5735, for computing the integrals the latter proposal predicts for the leading term in the expansion of the six-point remainder function, is extended to one of the subleading terms. In particular, we focus on the contribution of the two-gluon bound state in the dual flux tube picture, proving its general form at any order in the coupling, and providing explicit expressions up to six loops. These are included in the ancillary file accompanying the version of this paper on the arXiv.

EXACT S-MATRICES FOR AdS3/CFT2

We propose exact S-matrices for the AdS 3/ CFT 2 duality between type IIB strings on AdS 3×S3×M4 with M4 = S3×S1 or T4 and the corresponding two-dimensional conformal field theories. We fix the two-particle S-matrices on the basis of the symmetries su(1|1) and su(1|1)×su(1|1). A crucial justification comes from the derivation of the all-loop Bethe ansatz matching exactly the recent conjecture proposed by Babichenko et al. [J. High Energy Phys.1003, 058 (2010), arXiv:0912.1723 [hep-th]] and Ohlsson Sax and Stefanski, Jr. [J. High Energy Phys.1108, 029 (2011), arXiv:1106.2558 [hep-th]].