Johan Kallen

Bio: Johan Kallen is an academic researcher from Uppsala University. The author has contributed to research in topics: Yang–Mills theory & Instanton. The author has an hindex of 14, co-authored 21 publications receiving 1251 citations. Previous affiliations of Johan Kallen include University of Geneva.

The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere

Abstract: Based on the construction by Hosomichi, Seong and Terashima we consider N = 1 supersymmetric 5D Yang-Mills theory with matter on a five-sphere with radius r. This theory can be thought of as a deformation of the theory in flat space with deformation parameter r and this deformation preserves 8 supercharges. We calculate the full perturbative partition function as a function of $ {{{r} \left/ {{g_Y^2}} \right.}_M} $ , where $ {g_Y}_M $ is the Yang-Mills coupling, and the answer is given in terms of a matrix model. We perform the calculation using localization techniques. We also argue that in the large N-limit of this deformed 5D Yang-Mills theory this matrix model provides the leading contribution to the partition function and the rest is exponentially suppressed.

Twisted supersymmetric 5D Yang-Mills theory and contact geometry

Abstract: We extend the localization calculation of the 3D Chern-Simons partition func- tion over Seifert manifolds to an analogous calculation in five dimensions. We construct a twisted version of N = 1 supersymmetric Yang-Mills theory defined on a circle bundle over a four dimensional symplectic manifold. The notion of contact geometry plays a crucial role in the construction and we suggest a generalization of the instanton equations to five- dimensional contact manifolds. Our main result is a calculation of the full perturbative partition function on S 5 for the twisted supersymmetric Yang-Mills theory with different Chern-Simons couplings. The final answer is given in terms of a matrix model. Our construction admits generalizations to higher dimensional contact manifolds. This work is inspired by the work of Baulieu-Losev-Nekrasov from the mid 90’s, and in a way it is covariantization of their ideas for a contact manifold.

Twisted supersymmetric 5D Yang-Mills theory and contact geometry

Abstract: We extend the localization calculation of the 3D Chern-Simons partition function over Seifert manifolds to an analogous calculation in five dimensions. We construct a twisted version of N=1 supersymmetric Yang-Mills theory defined on a circle bundle over a four dimensional symplectic manifold. The notion of contact geometry plays a crucial role in the construction and we suggest a generalization of the instanton equations to five dimensional contact manifolds. Our main result is a calculation of the full perturbative partition function on a five sphere for the twisted supersymmetric Yang-Mills theory with different Chern-Simons couplings. The final answer is given in terms of a matrix model. Our construction admits generalizations to higher dimensional contact manifolds. This work is inspired by the work of Baulieu-Losev-Nekrasov from the mid 90's, and in a way it is covariantization of their ideas for a contact manifold.

Instanton effects and quantum spectral curves

Abstract: We study a spectral problem associated to the quantization of a spectral curve arising in local mirror symmetry. The perturbative WKB quantization condition is determined by the quantum periods, or equivalently by the refined topological string in the Nekrasov–Shatashvili (NS) limit. We show that the information encoded in the quantum periods is radically insufficient to determine the spectrum: there is an infinite series of instanton corrections, which are non-perturbative in \({\hbar}\), and lead to an exact WKB quantization condition. Moreover, we conjecture the precise form of the instanton corrections: they are determined by the standard or unrefined topological string free energy, and we test our conjecture successfully against numerical calculations of the spectrum. This suggests that the non-perturbative sector of the NS refined topological string contains information about the standard topological string. As an application of the WKB quantization condition, we explain some recent observations relating membrane instanton corrections in ABJM theory to the refined topological string.

N 3-behavior from 5D Yang-Mills theory

Abstract: In this note we derive N 3-behavior at large ’t Hooft coupling for the free energy of 5D maximally supersymmetric Yang-Mills theory on S 5. We also consider a Z k quiver of this model, as well as a model with M hypermultiplets in the fundamental representation. We compare the results to the supergravity description and comment on their relation.

Holomorphic blocks in three dimensions

Abstract: We decompose sphere partition functions and indices of three-dimensional $$ \mathcal{N} $$ = 2 gauge theories into a sum of products involving a universal set of “holomorphic blocks”. The blocks count BPS states and are in one-to-one correspondence with the theory’s massive vacua. We also propose a new, effective technique for calculating the holomorphic blocks, inspired by a reduction to supersymmetric quantum mechanics. The blocks turn out to possess a wealth of surprising properties, such as a Stokes phenomenon that integrates nicely with actions of three-dimensional mirror symmetry. The blocks also have interesting dual interpretations. For theories arising from the compactification of the six-dimensional (2, 0) theory on a three-manifold M, the blocks belong to a basis of wave-functions in analytically continued Chern-Simons theory on M. For theories engineered on branes in Calabi-Yau geometries, the blocks offer a non-perturbative perspective on open topological string partition functions.

Supersymmetric Field Theories on Three-Manifolds

Abstract: We construct supersymmetric field theories on Riemannian three-manifolds $ \mathcal{M} $ , focusing on $ \mathcal{N} $ = 2 theories with a U(1)R symmetry. Our approach is based on the rigid limit of new minimal supergravity in three dimensions, which couples to the flat-space supermultiplet containing the R-current and the energy-momentum tensor. The field theory on $ \mathcal{M} $ possesses a single supercharge if and only if $ \mathcal{M} $ admits an almost contact metric structure that satisfies a certain integrability condition. This may lead to global restrictions on $ \mathcal{M} $ , even though we can always construct one supercharge on any given patch. We also analyze the conditions for the presence of additional supercharges. In particular, two supercharges of opposite R-charge exist on every Seifert manifold. We present general supersymmetric Lagrangians on $ \mathcal{M} $ and discuss their flat-space limit, which can be analyzed using the R-current supermultiplet. As an application, we show how the flat-space two-point function of the energy-momentum tensor in $ \mathcal{N} $ = 2 superconformal theories can be calculated using localization on a squashed sphere.

Exploring curved superspace

Abstract: We extend our previous analysis of Riemannian four-manifolds $ \mathcal{M} $ admitting rigid supersymmetry to $ \mathcal{N} $ = 1 theories that do not possess a U(1) R symmetry. With one exception, we find that $ \mathcal{M} $ must be a Hermitian manifold. However, the presence of supersymmetry imposes additional restrictions. For instance, a supercharge that squares to zero exists, if the canonical bundle of the Hermitian manifold $ \mathcal{M} $ admits a nowhere vanishing, holomorphic section. This requirement can be slightly relaxed if $ \mathcal{M} $ is a torus bundle over a Riemann surface, in which case we obtain a supercharge that squares to a complex Killing vector. We also analyze the conditions for the presence of more than one supercharge. The exceptional case occurs when $ \mathcal{M} $ is a warped product S 3 × $ \mathbb{R} $ , where the radius of the round S 3 is allowed to vary along $ \mathbb{R} $ . Such manifolds admit two supercharges that generate the superalgebra OSp(1|2). If the S 3 smoothly shrinks to zero at two points, we obtain a squashed four-sphere, which is not a Hermitian manifold.