Abstract
Using the N = 4 topological reformulation of N = 2 strings, we compute all loop partition function for special compactifications of N = 2 strings as a function of target moduli. We also reinterpret N = 4 topological amplitudes in terms of slightly modified N = 2 topological amplitudes. We present some preliminary evidence for the conjecture that N = 2 strings is the large N limit of Holomorphic Yang-Mills in four dimensions.
Highlights
One of the simplest types of string theories is N = 2 string
We show that quite generally N = 4 topological strings, are a slightly modified form of N = 2 topological string amplitudes
Given that N = 2 string has finite number of particles it is a candidate for a search for a large N limit of a gauge theory. We look for this and find some preliminary evidence that the large N limit of Holomorphic Yang-Mills theory in 4 dimensions (2 complex dimensions)[5][6] is N = 2 strings
Summary
In other words it gives exactly the same result as the partition function for the highest instanton number of the N = 2 string (2.5) with the exception of the insertion of JLJR It was argued in [4] that this N = 2 topological amplitude vanishes even with this charge insertion. The formal complex dimension of M is (g − 1), it typically has a dimension bigger than (g − 1) In such cases the topological amplitude computation is done by considering the bundle V on M whose fibers are the anti-ghost zero modes which is H1(N ) where N is the pull back of the normal bundle piece of the tangent bundle on the manifold restricted to the holomorphic image of the Riemann surface. We have not computed V for T 2 × R2, which is relevant for g > 2 amplitudes
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