Elliptic genus of E-strings

Abstract

Abstract:We study a family of 2d N = (0, 4) gauge theories which describes at low energy the dynamics of E-strings, the M2-branes suspended between a pair of M5 and M9 branes. The gauge theory is engineered using a duality with type IIA theory, leading to the D2-branes suspended between an NS5-brane and 8 D8-branes on an O8-plane. We compute the elliptic genus of this family of theories, and find agreement with the known results for single and two E-strings. The partition function can in principle be computed for arbitrary number of E-strings, and we compute them explicitly for low numbers. We test our predictions against the partially known results from topological strings, as well as from the instanton calculus of 5d Sp(1) gauge theory. Given the relation to topological strings, our computation provides the all genus partition function of the refined topological strings on the canonical bundle over 1 2 K3.

Little strings and T-duality

“…Just like our IIA strings are closely related to the 'M-strings' of 6d (2, 0) CFT, the E 8 × E 8 little strings would be closely related to the so-called E-strings of the 6d (1, 0) CFT, with E 8 global symmetry [30,31]. The E-string elliptic genera have been recently studied in [32], from 2d (0, 4) gauge theories.…”

Testing 5d-6d dualities with fractional D-branes

“…We will briefly review the E-string theory [5][6][7][8]13], and their circle compactifications to the 5d Sp(1) gauge theory with 8 hypermultiplets. The E-string theory and 6d N = (1, 0) SCFT with Sp(1) gauge symmetry are well-studied in reference [2,13], and we will follow their idea.…”

“…The 6d N = (1, 0) SCFTs have a tensor multiplet and Sp(N ) gauge symmetry with N f = 2N + 8 fundamental hypermulitplets, and these can be Higgsed [2] to the E-string theory [5][6][7][8]. The 5d N = 1 gauge theories have Sp(N + 1) gauge symmetry and N f = 2N +8 fundamental hypermultiplets.…”

Little strings on D n orbifolds

“…It usually agrees with the string theory realization of instanton solitons and underlying gauge theories. The brane realization can also cover the particular case that little strings are E-strings, which do not carry any instanton charge, providing the UV gauge theory descriptions [22,23] for them. The resulting UV gauge theory is particularly useful to compute SUSY-protected observables, such as the elliptic genera of little strings.…”

“…These winding sectors correspond to multiple E-strings (for n = 4) or Sp(n − 4) instanton strings (for n > 4). Their elliptic genera are written in [22,23,[39][40][41][42]. For k 2 = 1,…”