A. Muñoz Mateo1,3,∗ Xiaoquan Yu2,3,† and Jun Nian4,5‡ 1 Departament de Fı́sica Quàntica i Astrofı... more A. Muñoz Mateo1,3,∗ Xiaoquan Yu2,3,† and Jun Nian4,5‡ 1 Departament de Fı́sica Quàntica i Astrofı́sica, Universitat de Barcelona, Martı́ i Franquès, 1, E–08028 Barcelona, Spain 2 Department of Physics, Centre for Quantum Science, and Dodd-Walls Centre for Photonic and Quantum Technologies, University of Otago, Dunedin, New Zealand 3New Zealand Institute for Advanced Study, Centre for Theoretical Chemistry and Physics,Massey University, Auckland 0745, New Zealand 4Institut des Hautes Études Scientifiques, Le Bois-Marie, 35 route de Chartres, 91440 Bures-sur-Yvette, France and 5C. N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, NY 11794-3840, United States
We demonstrate the existence of stationary states composed of vortex lines attached to planar dar... more We demonstrate the existence of stationary states composed of vortex lines attached to planar dark solitons in scalar Bose-Einstein condensates. Dynamically stable states of this type are found at low values of the chemical potential in channeled condensates, where the long-wavelength instability of dark solitons is prevented. In oblate, harmonic traps, U-shaped vortex lines attached by both ends to a single planar soliton are shown to be long-lived states. Our results are reported for parameters typical of current experiments, and open up a way to explore the interplay of different topological structures. These configurations provide Dirichlet boundary conditions for vortex lines and thereby mimic open strings attached to D-branes in string theory. We show that these similarities can be formally established by mapping the Gross-Pitaevskii theory into a dual effective string theory for open strings via a boson-vortex duality in 3+1 dimensions. Combining a one-form gauge field living on the soliton plane which couples to the endpoints of vortex lines and a two-form gauge field which couples to vortex lines, we obtain a gauge-invariant dual action of open vortex lines with their endpoints attached to dark solitons.
We compute the partition functions of N = 1 gauge theories on S 2 × R 2 ε using supersymmetric lo... more We compute the partition functions of N = 1 gauge theories on S 2 × R 2 ε using supersymmetric localization. The path integral reduces to a sum over vortices at the poles of S 2 and at the origin of R 2 ε . The exact partition functions allow us to test Seiberg duality beyond the supersymmetric index. We propose the N = 1 partition functions on the Ωbackground, and show that the Nekrasov partition functions can be recovered from these building blocks.
We compute the partition functions of N = 1 gauge theories on S^2 ×R^2_ε using supersymmetric loc... more We compute the partition functions of N = 1 gauge theories on S^2 ×R^2_ε using supersymmetric localization. The path integral reduces to a sum over vortices at the poles of S^2 and at the origin of R^2_ε. The exact partition functions allow us to test Seiberg duality beyond the supersymmetric index. We propose the N = 1 partition functions on the Ω-background, and show that the Nekrasov partition functions can be recovered from these building blocks.
We compute the partition functions of [Formula: see text] gauge theories on [Formula: see text] u... more We compute the partition functions of [Formula: see text] gauge theories on [Formula: see text] using supersymmetric localization. The path integral reduces to a sum over vortices at the poles of [Formula: see text] and at the origin of [Formula: see text]. The exact partition functions allow us to test Seiberg duality beyond the supersymmetric index. We propose the [Formula: see text] partition functions on the [Formula: see text]-background, and show that the Nekrasov partition functions can be recovered from these building blocks.
of the Dissertation Some Studies on Partition Functions in Quantum Field Theory and Statistical M... more of the Dissertation Some Studies on Partition Functions in Quantum Field Theory and Statistical Mechanics
We study a class of two-dimensional N = (2, 2) supersymmetric gauge theories, given by semichiral... more We study a class of two-dimensional N = (2, 2) supersymmetric gauge theories, given by semichiral multiplets coupled to the usual vector multiplet. In the UV, these theories are traditional gauge theories deformed by a gauged Wess-Zumino term. In the IR, they give rise to nonlinear sigma models on noncompact generalized Kähler manifolds, which contain a three-form field H and whose metric is not Kähler. We place these theories on S 2 and compute their partition function exactly with localization techniques. We find that the contribution of instantons to the partition function that we define is insensitive to the deformation, and discuss our results from the point of view of the generalized Kähler target space.
We study a class of two-dimensional N = (2, 2) supersymmetric gauge theories, given by semichiral... more We study a class of two-dimensional N = (2, 2) supersymmetric gauge theories, given by semichiral multiplets coupled to the usual vector multiplet. In the UV, these theories are traditional gauge theories deformed by a gauged Wess-Zumino term. In the IR, they give rise to nonlinear sigma models on noncompact generalized Kähler manifolds, which contain a three-form field H and whose metric is not Kähler. We place these theories on S 2 and compute their partition function exactly with localization techniques. We find that the contribution of instantons to the partition function that we define is insensitive to the deformation, and discuss our results from the point of view of the generalized Kähler target space.
In order to have a new perspective on the long-standing problem of the mass gap in Yang–Mills the... more In order to have a new perspective on the long-standing problem of the mass gap in Yang–Mills theory, we study in this paper the quantum Yang–Mills theory in the presence of topologically nontrivial backgrounds. The topologically stable gauge fields are constrained by the form invariance condition and the topological properties. Obeying these constraints, the known classical solutions to the Yang–Mills equation in the three- and four-dimensional Euclidean spaces are recovered, and the other allowed configurations form the nontrivial topological fluctuations at quantum level. Together, they constitute the background configurations, upon which the quantum Yang–Mills theory can be constructed. We demonstrate that the theory mimics the Higgs mechanism in a certain limit and develops a mass gap at semiclassical level on a flat space with finite size or on a sphere.
A. Muñoz Mateo1,3,∗ Xiaoquan Yu2,3,† and Jun Nian4,5‡ 1 Departament de Fı́sica Quàntica i Astrofı... more A. Muñoz Mateo1,3,∗ Xiaoquan Yu2,3,† and Jun Nian4,5‡ 1 Departament de Fı́sica Quàntica i Astrofı́sica, Universitat de Barcelona, Martı́ i Franquès, 1, E–08028 Barcelona, Spain 2 Department of Physics, Centre for Quantum Science, and Dodd-Walls Centre for Photonic and Quantum Technologies, University of Otago, Dunedin, New Zealand 3New Zealand Institute for Advanced Study, Centre for Theoretical Chemistry and Physics,Massey University, Auckland 0745, New Zealand 4Institut des Hautes Études Scientifiques, Le Bois-Marie, 35 route de Chartres, 91440 Bures-sur-Yvette, France and 5C. N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, NY 11794-3840, United States
We demonstrate the existence of stationary states composed of vortex lines attached to planar dar... more We demonstrate the existence of stationary states composed of vortex lines attached to planar dark solitons in scalar Bose-Einstein condensates. Dynamically stable states of this type are found at low values of the chemical potential in channeled condensates, where the long-wavelength instability of dark solitons is prevented. In oblate, harmonic traps, U-shaped vortex lines attached by both ends to a single planar soliton are shown to be long-lived states. Our results are reported for parameters typical of current experiments, and open up a way to explore the interplay of different topological structures. These configurations provide Dirichlet boundary conditions for vortex lines and thereby mimic open strings attached to D-branes in string theory. We show that these similarities can be formally established by mapping the Gross-Pitaevskii theory into a dual effective string theory for open strings via a boson-vortex duality in 3+1 dimensions. Combining a one-form gauge field living on the soliton plane which couples to the endpoints of vortex lines and a two-form gauge field which couples to vortex lines, we obtain a gauge-invariant dual action of open vortex lines with their endpoints attached to dark solitons.
We compute the partition functions of N = 1 gauge theories on S 2 × R 2 ε using supersymmetric lo... more We compute the partition functions of N = 1 gauge theories on S 2 × R 2 ε using supersymmetric localization. The path integral reduces to a sum over vortices at the poles of S 2 and at the origin of R 2 ε . The exact partition functions allow us to test Seiberg duality beyond the supersymmetric index. We propose the N = 1 partition functions on the Ωbackground, and show that the Nekrasov partition functions can be recovered from these building blocks.
We compute the partition functions of N = 1 gauge theories on S^2 ×R^2_ε using supersymmetric loc... more We compute the partition functions of N = 1 gauge theories on S^2 ×R^2_ε using supersymmetric localization. The path integral reduces to a sum over vortices at the poles of S^2 and at the origin of R^2_ε. The exact partition functions allow us to test Seiberg duality beyond the supersymmetric index. We propose the N = 1 partition functions on the Ω-background, and show that the Nekrasov partition functions can be recovered from these building blocks.
We compute the partition functions of [Formula: see text] gauge theories on [Formula: see text] u... more We compute the partition functions of [Formula: see text] gauge theories on [Formula: see text] using supersymmetric localization. The path integral reduces to a sum over vortices at the poles of [Formula: see text] and at the origin of [Formula: see text]. The exact partition functions allow us to test Seiberg duality beyond the supersymmetric index. We propose the [Formula: see text] partition functions on the [Formula: see text]-background, and show that the Nekrasov partition functions can be recovered from these building blocks.
of the Dissertation Some Studies on Partition Functions in Quantum Field Theory and Statistical M... more of the Dissertation Some Studies on Partition Functions in Quantum Field Theory and Statistical Mechanics
We study a class of two-dimensional N = (2, 2) supersymmetric gauge theories, given by semichiral... more We study a class of two-dimensional N = (2, 2) supersymmetric gauge theories, given by semichiral multiplets coupled to the usual vector multiplet. In the UV, these theories are traditional gauge theories deformed by a gauged Wess-Zumino term. In the IR, they give rise to nonlinear sigma models on noncompact generalized Kähler manifolds, which contain a three-form field H and whose metric is not Kähler. We place these theories on S 2 and compute their partition function exactly with localization techniques. We find that the contribution of instantons to the partition function that we define is insensitive to the deformation, and discuss our results from the point of view of the generalized Kähler target space.
We study a class of two-dimensional N = (2, 2) supersymmetric gauge theories, given by semichiral... more We study a class of two-dimensional N = (2, 2) supersymmetric gauge theories, given by semichiral multiplets coupled to the usual vector multiplet. In the UV, these theories are traditional gauge theories deformed by a gauged Wess-Zumino term. In the IR, they give rise to nonlinear sigma models on noncompact generalized Kähler manifolds, which contain a three-form field H and whose metric is not Kähler. We place these theories on S 2 and compute their partition function exactly with localization techniques. We find that the contribution of instantons to the partition function that we define is insensitive to the deformation, and discuss our results from the point of view of the generalized Kähler target space.
In order to have a new perspective on the long-standing problem of the mass gap in Yang–Mills the... more In order to have a new perspective on the long-standing problem of the mass gap in Yang–Mills theory, we study in this paper the quantum Yang–Mills theory in the presence of topologically nontrivial backgrounds. The topologically stable gauge fields are constrained by the form invariance condition and the topological properties. Obeying these constraints, the known classical solutions to the Yang–Mills equation in the three- and four-dimensional Euclidean spaces are recovered, and the other allowed configurations form the nontrivial topological fluctuations at quantum level. Together, they constitute the background configurations, upon which the quantum Yang–Mills theory can be constructed. We demonstrate that the theory mimics the Higgs mechanism in a certain limit and develops a mass gap at semiclassical level on a flat space with finite size or on a sphere.
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