Article
Physics, Particles & Fields
Cyril Closset, Horia Magureanu
Summary: We propose a new approach to computing the supersymmetric partition function on closed five-manifolds by introducing a non-trivial fibration over the four-manifold and examining the Coulomb branch partition function. We match the low-energy effective field theory approach to explicit one-loop computations and discuss the effects of non-perturbative particles. We also provide evidence for the validity of the Lockhart-Vafa formula for the five-sphere partition function.
JOURNAL OF HIGH ENERGY PHYSICS
(2023)
Article
Physics, Particles & Fields
M. Semenyakin
Summary: This paper discusses an important illustration in string theory, which is the tau-functions of integrable equations in the principle partition functions. It has been found that the (dual) partition functions of 4d N = 2 gauge theories can solve Painleve equations. Recent research has also suggested that the partition functions of topological string on local Calabi-Yau manifolds can solve q-difference equations of non-autonomous dynamics. The paper provides a detailed explanation of this proposal's solutions, presents a specific example, and suggests further research directions.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Min-xin Huang, Kimyeong Lee, Xin Wang
Summary: This paper proposes a refined topological string correspondence for the expectation values of half-BPS Wilson loop operators in 5d N=1 gauge theory partition function on the Omega-deformed background. The authors provide the refined topological vertex method and the refined holomorphic anomaly equation method to compute the partition functions of 5d Wilson loops in both A- and B-models. With the exact results in the B-model, they recover the quantum periods of local P-1 x P-1 model and local P-2 model in the study of quantum geometry and give a refined generalization of A-period.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Multidisciplinary
Taro Kimura, Fabrizio Nieri
Summary: By studying 5d supersymmetric gauge theories with unitary groups in the omega background and intersecting defects, we reveal the relationship between instanton and generalized vortex calculus. In a simplified scenario, we identify the dual supergroup theory for intersecting defects as the supergroup version of refined Chern-Simons theory via open/closed duality.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2021)
Article
Physics, Particles & Fields
Baptiste Filoche, Stefan Hohenegger
Summary: We discuss a class of Little String Theories (LSTs) whose low energy descriptions are supersymmetric gauge theories on the ω-background with gauge group U(N) and matter in the adjoint representation. We show that the instanton partition function of these theories can be written in terms of Kronecker-Eisenstein series, which in a particular limit of the deformation parameters of the ω-background organise themselves into Greens functions of free scalar fields on a torus.
We provide a concrete identification between (differences of) such propagators and Nekrasov subfunctions. The latter are also characterised by counting specific holomorphic curves in a Calabi-Yau threefold X-N,X-1 which engineers the LST. Furthermore, using the formulation of the partition function in terms of the Kronecker-Eisenstein series, we argue for new recursive structures which relate higher instanton contributions to products of lower ones.
JOURNAL OF HIGH ENERGY PHYSICS
(2023)
Article
Physics, Particles & Fields
Giuseppe Bogna, Lionel Mason
Summary: The construction of perturbative quantities on non-linear backgrounds allows for the inclusion of strong field effects in perturbation theory. In this study, we continue the effort to construct QFT observables on self-dual backgrounds in Yang-Mills theory, extending previous work on amplitudes to form factors and incorporating supersymmetry. Our analysis, based on reconstruction from data at null infinity, is closely related to research on celestial and twisted holography. We explore form factors in both pure Yang-Mills and their supersymmetric counterparts in N = 4 SYM, focusing on self-dual backgrounds. Using new formulae for lifting operators to twistor space, we derive tree-level MHV form factors around these backgrounds, providing simple dressings of the corresponding form factors around the vacuum. We also discuss the potential for going beyond the MHV sector by introducing dressed versions of the MHV diagram propagator, and we explore generating functionals and dual conformal representations of the MHV all plus 1-loop amplitude.
JOURNAL OF HIGH ENERGY PHYSICS
(2023)
Article
Physics, Particles & Fields
Fei Yan
Summary: In this study, we investigate the exact WKB method for the quantum Seiberg-Witten curve of 4d N = 2 pure SU(3) Yang-Mills in the language of abelianization. We explore the relevant differential equation, its solutions, and associated Stokes phenomena using the exact WKB method. Additionally, we investigate the exact quantization condition for a specific spectral problem. Our analysis also leads us to consider new Darboux coordinates on a moduli space of flat SL(3,C)-connections and numerical analysis supports the conjecture that these coordinates have asymptotic expansions given by the formal quantum periods series.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Alba Grassi, Zohar Komargodski, Luigi Tizzano
Summary: The study focuses on the correlation functions of Coulomb branch operators in four-dimensional N = 2 Superconformal Field Theories, particularly on rank-one theories. It is shown that the large charge limit of extremal correlators can be captured by a dual description of a chiral random matrix model of the Wishart-Laguerre type. This provides an analytic understanding of physics in specific excited states.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Particles & Fields
Tim Adamo, Anton Ilderton, Alexander J. MacLeod
Summary: For scattering amplitudes in strong background fields, it is possible to perturbatively expand the background to obtain higher-point vacuum amplitudes. In the case of self-dual plane wave backgrounds, the expansion for two-point, one-loop amplitudes in pure Yang-Mills, QED, and QCD reveals multicollinear limits of Hoop vacuum amplitudes, with only the all-plus helicity amplitude surviving. Furthermore, both abelian and non-abelian supersymmetric gauge theories show no helicity flip on any plane wave background, extending a known result in the Euler-Heisenberg limit of super-QED.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Particles & Fields
Renjan Rajan John, Sujoy Mahato, Madhusudhan Raman
Summary: The study focuses on the relationship between functions A and B of N = 2* gauge theories and topological invariants of the background, determining how multiplicative factors scale with the rank of the gauge group and the mass of the adjoint hypermultiplet through perturbative analysis.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Mathew Bullimore, Andrea E. Ferrari, Heeyeon Kim, Guangyu Xu
Summary: This paper investigates the contributions to the supersymmetric quantum mechanics from topological saddle points in supersymmetric localization of abelian gauge theories, providing further explanation for the twisted index of 3D N=2 gauge theories on S-1 x Sigma.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Particles & Fields
Max Hubner
Summary: The study explores the 4d minimally supersymmetric gauge theories derived from M-theory on local G(2)-manifolds, focusing on ALE-fibered G(2)-manifolds and the perspective of a partially twisted 7d supersymmetric Yang-Mills theory and its Higgs bundle. It was found that Euclidean M2-brane instantons lead to non-perturbative effects of the 7d supersymmetric Yang-Mills theory, corresponding to the instantons of a colored supersymmetric quantum mechanics. The contributions of M2-brane instantons to the 4d superpotential in the effective 7d description were computed via localization in the colored quantum mechanics, and non-split Higgs bundles were also considered for analysis of their 4d spectrum.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Particles & Fields
Daniele Dorigoni, Paolo Vallarino
Summary: This work explores the application of supersymmetric localization in N = 4 supersymmetric Yang-Mills theory. By combining lattice sum representation with Goddard-Nuyts-Olive duality, a unified two-dimensional lattice sum representation applicable to all simple gauge groups is provided. Formulas are proposed for both perturbative and non-perturbative expansions for simple gauge groups and common backgrounds. In addition, new results regarding exceptional gauge groups are obtained by deriving Laplace equations for the integrated correlators.
JOURNAL OF HIGH ENERGY PHYSICS
(2023)
Article
Physics, Particles & Fields
Dharmesh Jain, Arkajyoti Manna
Summary: In this study, a novel approach to uncovering Stokes phenomenon exhibited by the holomorphic blocks of the CP1 model is proposed by considering it as a specific decoupling limit of the SQED(2) model. By utilizing a Z(3) symmetry to transform holomorphic blocks, six pairs of SQED(2) holomorphic blocks are identified, covering the full parameter space of the SQED(2) model. These findings provide insights into the relationship between different pairs of holomorphic blocks and their associated Stokes-like regions.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Particles & Fields
Hynek Paul, Eric Perlmutter, Himanshu Raj
Summary: In this paper, we study a closed-form solution for a family of integrated four-point functions involving stress tensor multiplet composites of arbitrary R-charge in four-dimensional N = 4 super Yang-Mills theory with gauge group SU(N). We show that these integrated correlators are equivalent to a one-dimensional semi-infinite lattice of harmonic oscillators with nearest-neighbor interactions, evolving over the fundamental domain of SL(2, Z). The solution is exact in the R-charge p, rank N, and complexified gauge coupling tau, allowing for a systematic and non-perturbative large charge expansion.
JOURNAL OF HIGH ENERGY PHYSICS
(2023)