Supersymmetric quantum mechanics in one, two and three dimensions

We rederive the recently introduced N=2 topological gauge theories, representing the Euler characteristic of moduli spaces ℳ of connections, from supersymmetric quantum mechanics on the infinite-dimensional spaces [Formula: see text] of gauge orbits. To that end we discuss variants of ordinary supersymmetric quantum mechanics which have meaningful extensions to infinite-dimensional target spaces, and introduce supersymmetric quantum mechanics actions modeling the Riemannian geometry of submersions and embeddings, relevant to the projections [Formula: see text] and inclusions [Formula: see text] respectively. We explain the relation between Donaldson theory and the gauge theory of flat connections in three dimensions and illustrate the general construction by other two- and four-dimensional examples.

Download Full-text

Exact Analytical Solutions of the Non Polynomial Oscilator

Zeitschrift für Naturforschung A ◽

10.1515/zna-1988-0411 ◽

1988 ◽

Vol 43 (4) ◽

pp. 360-362 ◽

Cited By ~ 4

Author(s):

Pinaki Roy ◽

Rajkumar Roychoudhury

Keyword(s):

Quantum Mechanics ◽

Exact Solutions ◽

Analytical Solutions ◽

Supersymmetric Quantum Mechanics ◽

Coupling Constants ◽

Three Dimensions ◽

Exact Analytical Solutions

Abstract We derive new exact (analytical) solutions of the non polynomial oscillator V(x) = x2 + λx2 / (1 + g x2) in one as well in three dimensions. The solutions are derived within the framework of supersymmetric quantum mechanics, and it is shown that exact solutions exist when the coupling constants satisfy a supersymmetric constraint.

Download Full-text

Supersymmetric quantum mechanics

Particle Physics and the Schrödinger Equation ◽

10.1017/cbo9780511524394.005 ◽

1997 ◽

pp. 146-150

Keyword(s):

Quantum Mechanics ◽

Supersymmetric Quantum Mechanics

Download Full-text

QLB for Quantum Many-Body and Quantum Field Theory

10.1093/oso/9780199592357.003.0033 ◽

2018 ◽

Author(s):

Sauro Succi

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Quantum Mechanics ◽

Quantum Computing ◽

Single Particle ◽

Body Problem ◽

Three Dimensions ◽

Quantum Field ◽

Many Body ◽

Quantum Particles

Chapter 32 expounded the basic theory of quantum LB for the case of relativistic and non-relativistic wavefunctions, namely single-particle quantum mechanics. This chapter goes on to cover extensions of the quantum LB formalism to the overly challenging arena of quantum many-body problems and quantum field theory, along with an appraisal of prospective quantum computing implementations. Solving the single particle Schrodinger, or Dirac, equation in three dimensions is a computationally demanding task. This task, however, pales in front of the ordeal of solving the Schrodinger equation for the quantum many-body problem, namely a collection of many quantum particles, typically nuclei and electrons in a given atom or molecule.

Download Full-text

ABCD of ’t Hooft operators

Journal of High Energy Physics ◽

10.1007/jhep04(2021)241 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Hirotaka Hayashi ◽

Takuya Okuda ◽

Yutaka Yoshida

Keyword(s):

Quantum Mechanics ◽

Gauge Theories ◽

Supersymmetric Quantum Mechanics ◽

Type Ii ◽

Expectation Values ◽

String Theories

Abstract We compute by supersymmetric localization the expectation values of half-BPS ’t Hooft line operators in $$ \mathcal{N} $$ N = 2 U(N ), SO(N ) and USp(N ) gauge theories on S1 × ℝ3 with an Ω-deformation. We evaluate the non-perturbative contributions due to monopole screening by calculating the supersymmetric indices of the corresponding supersymmetric quantum mechanics, which we obtain by realizing the gauge theories and the ’t Hooft operators using branes and orientifolds in type II string theories.

Download Full-text

Topological correlators and surface defects from equivariant cohomology

Journal of High Energy Physics ◽

10.1007/jhep09(2020)185 ◽

2020 ◽

Vol 2020 (9) ◽

Author(s):

Rodolfo Panerai ◽

Antonio Pittelli ◽

Konstantina Polydorou

Keyword(s):

Quantum Mechanics ◽

Equivariant Cohomology ◽

Surface Defects ◽

Star Product ◽

Three Dimensional ◽

Three Dimensions ◽

Dimensional System ◽

The Novel ◽

One Dimensional ◽

Dual Quantum

Abstract We find a one-dimensional protected subsector of $$ \mathcal{N} $$ N = 4 matter theories on a general class of three-dimensional manifolds. By means of equivariant localization we identify a dual quantum mechanics computing BPS correlators of the original model in three dimensions. Specifically, applying the Atiyah-Bott-Berline-Vergne formula to the original action demonstrates that this localizes on a one-dimensional action with support on the fixed-point submanifold of suitable isometries. We first show that our approach reproduces previous results obtained on S3. Then, we apply it to the novel case of S2× S1 and show that the theory localizes on two noninteracting quantum mechanics with disjoint support. We prove that the BPS operators of such models are naturally associated with a noncom- mutative star product, while their correlation functions are essentially topological. Finally, we couple the three-dimensional theory to general $$ \mathcal{N} $$ N = (2, 2) surface defects and extend the localization computation to capture the full partition function and BPS correlators of the mixed-dimensional system.

Download Full-text

Local G2-manifolds, Higgs bundles and a colored quantum mechanics

Journal of High Energy Physics ◽

10.1007/jhep05(2021)002 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

Max Hübner

Keyword(s):

Quantum Mechanics ◽

Gauge Theories ◽

Supersymmetric Quantum Mechanics ◽

Higgs Bundle ◽

Higgs Bundles ◽

View Point ◽

Yang Mills ◽

G2 Manifolds ◽

Supersymmetric Gauge ◽

M Theory

Abstract M-theory on local G2-manifolds engineers 4d minimally supersymmetric gauge theories. We consider ALE-fibered G2-manifolds and study the 4d physics from the view point of a partially twisted 7d supersymmetric Yang-Mills theory and its Higgs bundle. Euclidean M2-brane instantons descend to non-perturbative effects of the 7d supersymmetric Yang-Mills theory, which are found to be in one to one correspondence with the instantons of a colored supersymmetric quantum mechanics. We compute the contributions of M2-brane instantons to the 4d superpotential in the effective 7d description via localization in the colored quantum mechanics. Further we consider non-split Higgs bundles and analyze their 4d spectrum.

Download Full-text