6d string chains

Abhijit Gadde,Seok Kim,Cumrun Vafa,Joonho Kim,Guglielmo Lockhart,Babak Haghighat

doi:10.1007/jhep02(2018)143

6d string chains

Abhijit Gadde, Seok Kim + Show 4 more

Open Access

https://doi.org/10.1007/jhep02(2018)143

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Abstract

We consider bound states of strings which arise in 6d (1,0) SCFTs that are realized in F-theory in terms of linear chains of spheres with negative self-intersections 1,2, and 4. These include the strings associated to N small E8 instantons, as well as the ones associated to M5 branes probing A and D type singularities in M-theory or D5 branes probing ADE singularities in Type IIB string theory. We find that these bound states of strings admit (0,4) supersymmetric quiver descriptions and show how one can compute their elliptic genera.

Highlights

Are arranged into trees according to specific rules
These include the strings associated to N small E8 instantons, as well as the ones associated to M5 branes probing A and D type singularities in M-theory or D5 branes probing ADE singularities in Type IIB string theory
In this paper we extend the list of theories for which such a description is available to three additional classes of 6d SCFTs:

Summary

Chains of strings

We are interested in computing the elliptic genera of the strings that arise on tensor branches of 6d (1, 0) SCFTs with several tensor multiplets, along the lines of [11], and. In this paper we aim to obtain 2d quiver gauge theories for a variety of 6d SCFTs that arise within M- and F-theory. The gauge groups arising in the theories discussed in this paper are either unitary, symplectic, or orthogonal. Let us identify the Cartan of SU(2) as follows: U(1) + × U(1) − × U(1)m × U(1)R ⊂ SU(2)A × SU(2)A × SU(2)Y × SU(2)A, where we identify U(1)R with the R-symmetry group of the (0, 4) theory when viewed as a (0, 2) theory. 1. To each gauge node i corresponds the following field content valued in representations of Gi (corresponding to ni strings of the ith kind): a vector multiplet Υi; a Fermi multiplet ΛΦi ; and two chiral multiplets Bi, Bi. The representation R is the adjoint representation whenever the gauge group is unitary, symmetric whenever the gauge node is orthogonal, and anti-symmetric if the gauge group is symplectic. Between each gauge node i and any successive node j one has a Fermi multiplet ΛQij; between the same gauge node i and any preceding node j one has a Fermi multiplet ΛQji

Partition functions of M5 branes probing ADE Singularities

Multiple M5 branes probing an M9 wall

Two-dimensional quiver

D5 branes probing ADE singularities