Universal features of BPS strings in six-dimensional SCFTs

Abstract

In theories with extended supersymmetry the protected observables of UV superconformal fixed points are found in a number of contexts to be encoded in the BPS solitons along an IR Coulomb-like phase. For six-dimensional SCFTs such a role is played by the BPS strings on the tensorial Coulomb branch. In this paper we develop a uniform description of the worldsheet theories of a BPS string for rank-one 6d SCFTs. These strings are the basic constituents of the BPS string spectrum of arbitrary rank six-dimensional models, which they generate by forming bound states. Motivated by geometric engineering in F-theory, we describe the worldsheet theories of the BPS strings in terms of topologically twisted 4d N = 2 theories in the presence of 1/2-BPS 2d (0, 4) defects. As the superconformal point of a 6d theory with gauge group G is approached, the resulting worldsheet theory flows to an N = (0, 4) NLSM with target the moduli space of one G instanton, together with a nontrivial left moving bundle characterized by the matter content of the six-dimensional model. We compute the anomaly polynomial and central charges of the NLSM, and argue that the 6d flavor symmetry F is realized as a current algebra on the string, whose level we compute. We find evidence that for generic theories the G dependence is captured at the level of the elliptic genus by characters of an affine Kac-Moody algebra at negative level, which we interpret as a subsector of the chiral algebra of the BPS string worldsheet theory. We also find evidence for a spectral flow relating the R-R and NS-R elliptic genera. These properties of the string CFTs lead to constraints on their spectra, which in combination with modularity allow us to determine the elliptic genera of a vast number of string CFTs, leading also to novel results for 6d and 5d instanton partition functions.

The Higgs mechanism — Hasse diagrams for symplectic singularities

“…While the global symmetry conjecture of Section 3.2 is satisfied in most cases, some of the global symmetries listed in [41,Tab. 1] are difficult to interpret from partial Higgsing.…”

Elliptic blowup equations for 6d SCFTs. Part II. Exceptional cases

“…Since the number of different embeddings is |P : Q ∨ |, the total number of non-equivalent blowup equations is n|P : Q ∨ |. The function A ω (m) is composed of θ 1 and η functions, see (3.5) [23,34] E1 [35,36] E1 with fugacities off [35,37] as the natural elliptic lift of the K-theoretic blowup equations for 5d gauge theories [16,28]. Moreover, the unity elliptic blowup equations in (1.5) ultimately lead to a complete solution of the elliptic genera E d in terms of an universal recursion formula, as will be shown in (3.32).…”

“…These exponential factors are determined by the index polynomial of each term, which as 18 Here qj ≡ exp(2πi j ) j = 1, 2 and q l ≡ q1/q2, qr ≡ √ q1q2. We will also use v ≡ qr, x ≡ q l in Section 4 and 5 to make contact with the literature such as [35,37]. a consequence of section 3.1, should be identical.…”

“…One can also see the symmetry (4.26) on the two sides of the ray with slop −1/2. Here the L Q τ ) function can be defined by all the red number inTable 13with the red +1 and +29 moving out, as they come from n = 137 Here the dependence on Qτ and Qm are implied. term in the summation.…”

Chiral algebras from Ω-deformation

“…A three-dimensional analog of this mechanism has been considered in[7]. A similar construction has also appeared in[30] in the context of BPS strings in six-dimensional SCFTs.…”