We obtain the elliptic curve and the Seiberg-Witten differential for an N = 2 superconformal field theory which has an E 8 global symmetry at the strong coupling point τ = e πi/3 .The differential has 120 poles corresponding to half the charged states in the fundamental representation of E 8 , with the other half living on the other sheet. Using this theory, we flow down to E 7 , E 6 and D 4 . A new feature is a λ SW for these theories based on their adjoint representations. We argue that these theories have different physics than those with λ SW built from the fundamental representations.10/96
We study certain properties of six-dimensional tensionless E-strings (arising from zero size E 8 instantons). In particular we show that n E-strings form a bound string which carries an E 8 level n current algebra as well as a left-over conformal system with c = 12n − 4 − 248n n+30 , whose characters can be computed. Moreover we show that the characters of the n-string bound state are captured by N = 4 U (n) topological Yang-Mills theory on 1 2 K3. This relation not only illuminates certain aspects of E-strings but can also be used to shed light on the properties of N = 4 topological Yang-Mills theories on manifolds with b + 2 = 1. In particular the E-string partition functions, which can be computed using local mirror symmetry on a Calabi-Yau three-fold, give the Euler characteristics of the YangMills instanton moduli space on 1 2 K3. Moreover, the partition functions are determined by a gap condition combined with a simple recurrence relation which has its origins in a holomorphic anomaly that has been conjectured to exist for N = 4 topological Yang-Mills on manifolds with b + 2 = 1 and is also related to the holomorphic anomaly for higher genus topological strings on Calabi-Yau threefolds.February, 1998
We show that almost all string theories, including the bosonic string, the superstring and W -string theories, possess a twisted N = 2 superconformal symmetry. This enables us to establish a connection between topological gravity and the field theoretical description of matter coupled to gravity. We also show how the BRST operators of the W n -string can be obtained by hamiltonian reduction of SL(n|n − 1). The tachyonic and ground ring states of W -strings are described in the light of the N = 2 superconformal structure, and the ground ring generators for the non-critical W 3 -string are explicitly constructed. The relationship to G/G models and quantum integrable systems is also briefly described.
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