Instanton worldlines in five-dimensional Ω-deformed gauge theory

Abstract

We discuss the Bosonic sector of a class of supersymmetric non-Lorentzian five-dimensional gauge field theories with an SU(1, 3) conformal symmetry. These actions have a Lagrange multiplier which imposes a novel Ω-deformed anti-self-dual gauge field constraint. Using a generalised ’t Hooft ansatz we find the constraint equation linearizes allowing us to construct a wide class of explicit solutions. These include finite action configurations that describe worldlines of anti-instantons which can be created and annihilated. We also describe the dynamics on the constraint surface.

Five-dimensional path integrals for six-dimensional conformal field theories

“…Then, the integral of the Chern-Simons 3-form on any S 3 through which such a string is threaded is quantised, ensuring that (3.1) is satisfied. Gauge field configurations with precisely this form were found in [18], but we will not need their details here.…”

“…Further, note that configurations defined over R 5 which feature an arbitrary number of instanton insertions at points x a , as well as vanishing flux on S 4 ∞ as in (3.2), were found in [18]. Such configurations additionally satisfy the constraint…”

“…Indeed a Lagrangian may only manifestly realise some subgroup of the symmetries of the full JHEP02(2022)151 quantum theory, as previously demonstrated by the ABJM theory for M2-branes [13]. In a recent series of papers we have constructed a class of five-dimensional Lagrangians with 12 or 24 superconformal symmetries and a non-Lorentzian SU (1,3) spacetime symmetry [14][15][16], studied their correlators [17] and constructed explicit instanton solutions [18]. In this paper we make a proposal as to how these can be used to provide a path integral construction of correlators of six-dimensional superconformal field theories such as the (2, 0) theory associated to M5-branes.…”

Non-Lorentzian $SU(1,n)$ Spacetime Symmetry in Various Dimensions

“…It is interesting to note that this condition appears to be manifestly realised in known supersymmetric interacting gauge theory examples of su(1, 3) theories [10], in a rather novel way. In particular, in such theories, P + is identified as instanton charge, and the dynamics are constrained such that only anti-instantons, corresponding to p + ≤ 0, are allowed to propagate [12].…”

“…Further, note that a class of non-Abelian gauge theories in five-dimensions with u(1) ⊕ su(1, 3) symmetry and realising precisely the full set of supersymmetries discussed above have been studied in detail [6,7,10,12,13]. In particular, in these models the Kaluza-Klein momentum P + is realised as instanton number, with the realisation of the full non-Abelian six-dimensional (2, 0) theory proposed through the inclusion of instanton operators.…”