We study the BPS spectrum and walls of marginal stability of the N = 2 supersymmetric theory in f... more We study the BPS spectrum and walls of marginal stability of the N = 2 supersymmetric theory in four dimensions with gauge group SU (n) and n ≤ N f < 2n fundamental flavours at the root of the Higgs branch. The strong-coupling spectrum of this theory was conjectured in hep-th/9902134 to coincide with that of the two-dimensional supersymmetric CP 2n−N f −1 sigma model. Using the Kontsevich-Soibelman wall-crossing formula, we start with the conjectured strong-coupling spectrum and extrapolate it to all other regions of the moduli space. In the weakcoupling regime, our results precisely agree with the semiclassical analysis of hep-th/9902134: in addition to the usual dyons, quarks, and W bosons, if the complex masses obey a particular inequality, the resulting weak-coupling spectrum includes a tower of bound states consisting of a dyon and one or more quarks. In the special case of Z n -symmetric masses, there are bound states with one quark for odd n and no bound states for even n. arXiv:1202.5595v1 [hep-th]
We study the interplay between wall-crossing in four-dimensional gauge theory and instanton contr... more We study the interplay between wall-crossing in four-dimensional gauge theory and instanton contributions to the moduli space metric of the same theory on R 3 × S 1 . We consider N = 2 SUSY Yang-Mills with gauge group SU (n) and focus on walls of marginal stability which extend to weak coupling. By comparison with explicit field theory results we verify the Kontsevich-Soibelman formula for the change in the BPS spectrum at these walls and check the smoothness of the metric in the corresponding compactified theory. We also verify in detail the predictions for the one instanton contribution to the metric coming from the non-linear integral equations of Gaiotto, Moore and Nietzke.
We study the quantum effects on the Coulomb branch of N = 2 SU (2) supersymmetric Yang-Mills with... more We study the quantum effects on the Coulomb branch of N = 2 SU (2) supersymmetric Yang-Mills with fundamental matters compactified on R 3 × S 1 , and extract the explicit perturbative and leading non-perturbative corrections to the moduli space metric predicted from the recent work of Gaiotto, Moore and Neitzke on wall-crossing [1]. We verify the predicted metric by computing the leading weak coupling instanton contribution to the four fermion correlation using standard field theory techniques, and demonstrate perfect agreement. We also demonstrate how previously known three dimensional quantities can be recovered in appropriate small radius limit, and provide a simple geometric picture from brane construction.
We calculate the leading weak-coupling instanton contribution to the moduli-space metric of N = 2... more We calculate the leading weak-coupling instanton contribution to the moduli-space metric of N = 2 supersymmetric Yang-Mills theory with gauge group SU (2) compactified on R 3 × S 1 . The results are in precise agreement with the semiclassical expansion of the exact metric recently conjectured by Gaiotto, Moore and Neitzke based on considerations related to wall-crossing in the corresponding four-dimensional theory.
We study the BPS spectrum and walls of marginal stability of the N = 2 supersymmetric theory in f... more We study the BPS spectrum and walls of marginal stability of the N = 2 supersymmetric theory in four dimensions with gauge group SU (n) and n ≤ N f < 2n fundamental flavours at the root of the Higgs branch. The strong-coupling spectrum of this theory was conjectured in hep-th/9902134 to coincide with that of the two-dimensional supersymmetric CP 2n−N f −1 sigma model. Using the Kontsevich-Soibelman wall-crossing formula, we start with the conjectured strong-coupling spectrum and extrapolate it to all other regions of the moduli space. In the weakcoupling regime, our results precisely agree with the semiclassical analysis of hep-th/9902134: in addition to the usual dyons, quarks, and W bosons, if the complex masses obey a particular inequality, the resulting weak-coupling spectrum includes a tower of bound states consisting of a dyon and one or more quarks. In the special case of Z n -symmetric masses, there are bound states with one quark for odd n and no bound states for even n. arXiv:1202.5595v1 [hep-th]
We study the interplay between wall-crossing in four-dimensional gauge theory and instanton contr... more We study the interplay between wall-crossing in four-dimensional gauge theory and instanton contributions to the moduli space metric of the same theory on R 3 × S 1 . We consider N = 2 SUSY Yang-Mills with gauge group SU (n) and focus on walls of marginal stability which extend to weak coupling. By comparison with explicit field theory results we verify the Kontsevich-Soibelman formula for the change in the BPS spectrum at these walls and check the smoothness of the metric in the corresponding compactified theory. We also verify in detail the predictions for the one instanton contribution to the metric coming from the non-linear integral equations of Gaiotto, Moore and Nietzke.
We study the quantum effects on the Coulomb branch of N = 2 SU (2) supersymmetric Yang-Mills with... more We study the quantum effects on the Coulomb branch of N = 2 SU (2) supersymmetric Yang-Mills with fundamental matters compactified on R 3 × S 1 , and extract the explicit perturbative and leading non-perturbative corrections to the moduli space metric predicted from the recent work of Gaiotto, Moore and Neitzke on wall-crossing [1]. We verify the predicted metric by computing the leading weak coupling instanton contribution to the four fermion correlation using standard field theory techniques, and demonstrate perfect agreement. We also demonstrate how previously known three dimensional quantities can be recovered in appropriate small radius limit, and provide a simple geometric picture from brane construction.
We calculate the leading weak-coupling instanton contribution to the moduli-space metric of N = 2... more We calculate the leading weak-coupling instanton contribution to the moduli-space metric of N = 2 supersymmetric Yang-Mills theory with gauge group SU (2) compactified on R 3 × S 1 . The results are in precise agreement with the semiclassical expansion of the exact metric recently conjectured by Gaiotto, Moore and Neitzke based on considerations related to wall-crossing in the corresponding four-dimensional theory.
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Papers by Kirill Petunin