scholarly journals Leibniz rule and exact supersymmetry on the lattice: the case of supersymmetric quantum mechanics

2005 ◽  
Author(s):  
Hiroto So ◽  
Mitsuhiro Kato ◽  
Makoto Sakamoto
Keyword(s):  
Quantum Mechanics ◽  
Supersymmetric Quantum Mechanics ◽  
Leibniz Rule

scholarly journals ON SUPERGROUPS WITH ODD CLIFFORD PARAMETERS AND SUPERSYMMETRY WITH MODIFIED LEIBNIZ RULE

2008 ◽  
Vol 23 (02) ◽  
pp. 309-326 ◽  
Author(s):  
Z. KUZNETSOVA ◽  
M. ROJAS ◽  
F. TOPPAN
Keyword(s):  
Quantum Mechanics ◽  
Supersymmetric Quantum Mechanics ◽  
Auxiliary Field ◽  
Leibniz Rule ◽  
Drinfeld Twist ◽  
Covariant Derivatives ◽  
Supersymmetric Theories ◽  
Equations Of Motions

We investigate supergroups with Grassmann parameters replaced by odd Clifford parameters. The connection with nonanticommutative supersymmetry is discussed. A Berezin-like calculus for odd Clifford variables is introduced. Fermionic covariant derivatives for supergroups with odd Clifford variables are derived. Applications to supersymmetric quantum mechanics are made. Deformations of the original supersymmetric theories are encountered when the fermionic covariant derivatives do not obey the graded Leibniz property. The simplest nontrivial example is given by the N = 2 supersymmetric quantum mechanics with a real (1, 2, 1) multiplet and a cubic potential. The action is real. Depending on the overall sign ("Euclidean" or "Lorentzian") of the deformation, a Bender–Boettcher pseudo-Hermitian Hamiltonian is encountered when solving the equations of motions of the auxiliary field. A possible connection of our framework with the Drinfeld twist deformation of supersymmetry is pointed out.

scholarly journals ABCD of ’t Hooft operators

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.

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

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.

scholarly journals Wronskian differential formula for confluent supersymmetric quantum mechanics

2012 ◽  
Vol 376 (5) ◽  
pp. 692-696 ◽  
Author(s):  
David Bermudez ◽  
David J. Fernández C. ◽  
Nicolás Fernández-García
Keyword(s):  
Quantum Mechanics ◽  
Supersymmetric Quantum Mechanics

A Golden-Thompson inequality in supersymmetric quantum mechanics

1991 ◽  
Vol 21 (3) ◽  
pp. 237-244 ◽  
Author(s):  
Slawomir Klimek ◽  
Andrzej Lesniewski
Keyword(s):  
Quantum Mechanics ◽  
Supersymmetric Quantum Mechanics
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