Abstract
In this work, I study the deformation of the topological string by Ω¯, the complex conjugate of the Ω-deformation. Namely, I identify Ω¯ in terms of a physical state in the string spectrum and verify that the deformed Yang-Mills and ADHM actions are reproduced. This completes the study initiated in [1] where we show that Ω¯ decouples from the one-loop topological amplitudes in heterotic string theory. Similarly to the N=2⋆ deformation, I show that the quadratic terms in the effective action play a crucial role in obtaining the correct realisation of the full Ω-deformation. Finally, I comment on the differences between the graviphoton and the Ω-deformation in general and discuss possible Ω¯ remnants at the boundary of the string moduli space.
Highlights
Little attention has been devoted to the study of the -background as a non-holomorphic deformation at the string level
If one denotes 1,2 the two parameters of the latter, for 1 + 2 = 0 the -deformed gauge theory partition function is the field theory limit of the topological string partition function Fg [5] which computes a class of higher derivative gravitational couplings in the effective action [6]
I prove that this ansatz is correct by showing that it leads to the correct effective actions in field theory
Summary
Little attention has been devoted to the study of the -background as a non-holomorphic deformation at the string level. It is non-holomorphic in the sense that it has a holomorphic as well as an anti-holomorphic part denoted The latter decouples from physical observables and this is clear from the localisation perspective whereis a Q-exact deformation of the effective action. The connection between string amplitudes and supersymmetric gauge theories has been further extended beyond topological limit [7,8,9] In all these studies, the antiholomorphic partis implicitly set to zero. I prove that this ansatz is correct by showing that it leads to the correct effective actions in field theory This is done by coupling the open string degrees of freedom of a Dp-D(p+4) system in type I string theory to the closed string background using similar techniques as in [8,11,12]. To keep the discussion clear, several technical aspects and useful results are presented in two appendices
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