Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-06-17
Physics
High Energy Physics
High Energy Physics - Theory
32 pages, 8 figures
Scientific paper
Four dimensional $N=2$ generalized superconformal field theory can be defined by compactifying six dimensional $(0,2)$ theory on a Riemann surface with regular punctures. In previous studies, gauge coupling spaces of those theories are identified with the moduli space of Riemann surface with marked points $M_{g,n}$. We show that the weakly coupled gauge group description corresponds to a stable nodal curve and different duality frames correspond to different stable nodal curves of the same punctured Riemann surface, so the coupling space is indeed Deligne-Mumford compactification $\bar{M}_{g,n}$. We also give an algorithm to determine the weakly coupled gauge group and the new appearing puncture if the gauge group is completely decoupled, similarly we can also determine the matter ending only on this gauge group. The same nodal curve can be used to represent the conformal block of two dimensional conformal field theory, therefore we establish an one to one correspondence between the conformal block of 2d theory in a certain channel and the weakly coupled 4d theory. The information about the gauge group tells us what is the intermediate state in the conformal block. We can also determine whether the correlation function of 2d theory can be written as the product of three point functions and the conformal block using gauge theory.
Nanopoulos Dimitri
Xie Dan
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