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 Local Mathematics and No Information at a Distance; Some Effects on Physics and Geometry

Proceedings ◽  
2020 ◽  
Vol 47 (1) ◽  
pp. 3
Author(s):  
Paul Benioff
Keyword(s):  
Quantum Mechanics ◽  
Gauge Theories ◽  
Expectation Values ◽  
Space And Time ◽  
Geometric Systems ◽  
Path Lengths ◽  
Time Point ◽  
Mathematical Systems

Local mathematics consists of a collection of mathematical systems located at each space and time point. The collection is limited to the systems that include numbers in their axiomatic description. A scalar map between systems at different locations is based on the distinction of two conflated concepts, number and number value. The effect that this setup has on theory descriptions of physical and geometric systems is described. This includes a scalar spin 0 field in gauge theories, expectation values in quantum mechanics and path lengths in geometry. The possible relation of the scalar map to consciousness is noted.

scholarly journals TOPOLOGICAL GAUGE THEORIES FROM SUPERSYMMETRIC QUANTUM MECHANICS ON SPACES OF CONNECTIONS

1993 ◽  
Vol 08 (03) ◽  
pp. 573-585 ◽  
Author(s):  
MATTHIAS BLAU ◽  
GEORGE THOMPSON
Keyword(s):  
Quantum Mechanics ◽  
Gauge Theory ◽  
Euler Characteristic ◽  
Moduli Spaces ◽  
Riemannian Geometry ◽  
Gauge Theories ◽  
Supersymmetric Quantum Mechanics ◽  
Three Dimensions ◽  
Flat Connections ◽  
Infinite Dimensional

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.

scholarly journals Local Mathematics and No Information at a Distance; Some Effects on Physics and Geometry

Proceedings ◽  
2020 ◽  
Vol 47 (1) ◽  
pp. 3
Author(s):  
Paul Benioff
Keyword(s):  
Quantum Mechanics ◽  
Gauge Theories ◽  
Expectation Values ◽  
Space And Time ◽  
Geometric Systems ◽  
Path Lengths ◽  
Time Point ◽  
Mathematical Systems

Local mathematics consists of a collection of mathematical systems located at each space and time point. The collection is limited to the systems that include numbers in their axiomatic description. A scalar map between systems at different locations is based on the distinction of two conflated concepts, number and number value. The effect that this setup has on theory descriptions of physical and geometric systems is described. This includes a scalar spin 0 field in gauge theories, expectation values in quantum mechanics and path lengths in geometry. The possible relation of the scalar map to consciousness is noted.

scholarly journals WHAT DOES E8 KNOW ABOUT 11 DIMENSIONS?

2000 ◽  
Vol 15 (13) ◽  
pp. 851-856
Author(s):  
IAN I. KOGAN ◽  
JOHN F. WHEATER
Keyword(s):  
Quantum Mechanics ◽  
String Theory ◽  
Gauge Group ◽  
Gauge Theories ◽  
Dimensional Space ◽  
Supersymmetric Quantum Mechanics ◽  
Gauge Invariant ◽  
M Theory

We discuss some possible relationships in gauge theories, string theory and M-theory in the light of some recent results obtained in gauge-invariant supersymmetric quantum mechanics. In particular, this reveals a new relationship between the gauge group E8 and 11-dimensional space.

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
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