GENERALIZED RICCI FLOW AND SUPERGRAVITY VACUUM SOLUTIONS

We first give a proof that the supersymmetric configurations satisfy the equations of motion for type II supergravity. In flux compactifications, the string vacua preserving N = 2 supersymmetry are the twisted generalized Calabi–Yau manifold. The modulus space of the string vacua can be constructed. We discuss the generalized Dirac operator which adds a torsional term to the ordinary Dirac operator and compute its index by the path integral method. Via the variation of the action of supergravity one can introduce the generalized Ricci flow equations. We consider deforming the manifold with the generalized Ricci flow. Finally, we consider the linear stability of the fixed points of the generalized Ricci flow.

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"SCHWINGER MODEL" ON THE FUZZY SPHERE

Modern Physics Letters A ◽

10.1142/s0217732310034079 ◽

2010 ◽

Vol 25 (37) ◽

pp. 3151-3167 ◽

Cited By ~ 3

Author(s):

E. HARIKUMAR

Keyword(s):

Partition Function ◽

Field Strength ◽

Dirac Operator ◽

Path Integral ◽

Integral Method ◽

Gauge Fields ◽

Fuzzy Sphere ◽

Schwinger Model ◽

Spinor Fields ◽

Path Integral Method

In this paper, we construct a model of spinor fields interacting with specific gauge fields on the fuzzy sphere and analyze the chiral symmetry of this "Schwinger model". In constructing the theory of gauge fields interacting with spinors on the fuzzy sphere, we take the approach that the Dirac operator Dq on the q-deformed fuzzy sphere [Formula: see text] is the gauged Dirac operator on the fuzzy sphere. This introduces interaction between spinors and specific one-parameter family of gauge fields. We also show how to express the field strength for this gauge field in terms of the Dirac operators Dq and D alone. Using the path integral method, we have calculated the 2n-point functions of this model and show that, in general, they do not vanish, reflecting the chiral non-invariance of the partition function.

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Gauge Interactions

10.1093/oso/9780192844200.003.0013 ◽

2021 ◽

pp. 273-286

Author(s):

J. Iliopoulos ◽

T.N. Tomaras

Keyword(s):

Quantum Electrodynamics ◽

Integral Method ◽

Equations Of Motion ◽

Internal Symmetry ◽

Symmetry Groups ◽

Yang Mills ◽

Path Integral Method ◽

Popov Ghost ◽

Mills Field ◽

Matter Fields

The principle of gauge symmetry is introduced as a consequence of the invariance of the equations of motion under local transformations. We apply it to Abelian, as well as non-Abelian, internal symmetry groups. We derive in this way the Lagrangian of quantum electrodynamics and that of Yang–Mills theories. We quantise the latter using the path integral method and show the need for unphysical Faddeev–Popov ghost fields. We exhibit the geometric properties of the theory by formulating it on a discrete space-time lattice. We show that matter fields live on lattice sites and gauge fields on oriented lattice links. The Yang–Mills field strength is related to the curvature in field space.

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Path Integral Method in the Mean-field Model for the Magnetic Vector Potential

Geomagnetism and Aeronomy ◽

10.1134/s0016793220070300 ◽

2020 ◽

Vol 60 (7) ◽

pp. 989-992

Author(s):

E. V. Yushkov ◽

C. R. Kamaletdinov ◽

D. D. Sokoloff

Keyword(s):

Path Integral ◽

Vector Potential ◽

Integral Method ◽

Field Model ◽

Mean Field ◽

Magnetic Vector Potential ◽

Magnetic Vector ◽

Mean Field Model ◽

The Mean ◽

Path Integral Method

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Source Apportionment of the Anthropogenic Increment to Ozone, Formaldehyde, and Nitrogen Dioxide by the Path-Integral Method in a 3D Model

Environmental Science & Technology ◽

10.1021/acs.est.5b00467 ◽

2015 ◽

Vol 49 (11) ◽

pp. 6751-6759 ◽

Cited By ~ 9

Author(s):

Alan M. Dunker ◽

Bonyoung Koo ◽

Greg Yarwood

Keyword(s):

Nitrogen Dioxide ◽

Source Apportionment ◽

Path Integral ◽

Integral Method ◽

3D Model ◽

Path Integral Method

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Nothing is certain in string compactifications

Journal of High Energy Physics ◽

10.1007/jhep12(2020)032 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Iñaki García Etxebarria ◽

Miguel Montero ◽

Kepa Sousa ◽

Irene Valenzuela

Keyword(s):

Flux Compactifications ◽

Spin Structure ◽

Energy Condition ◽

Low Energy ◽

Type Ii ◽

String Compactifications ◽

Compact Dimension ◽

Bordism Group ◽

Topological Obstruction ◽

M Theory

Abstract A bubble of nothing is a spacetime instability where a compact dimension collapses. After nucleation, it expands at the speed of light, leaving “nothing” behind. We argue that the topological and dynamical mechanisms which could protect a compactification against decay to nothing seem to be absent in string compactifications once supersymmetry is broken. The topological obstruction lies in a bordism group and, surprisingly, it can disappear even for a SUSY-compatible spin structure. As a proof of principle, we construct an explicit bubble of nothing for a T3 with completely periodic (SUSY-compatible) spin structure in an Einstein dilaton Gauss-Bonnet theory, which arises in the low-energy limit of certain heterotic and type II flux compactifications. Without the topological protection, supersymmetric compactifications are purely stabilized by a Coleman-deLuccia mechanism, which relies on a certain local energy condition. This is violated in our example by the nonsupersymmetric GB term. In the presence of fluxes this energy condition gets modified and its violation might be related to the Weak Gravity Conjecture.We expect that our techniques can be used to construct a plethora of new bubbles of nothing in any setup where the low-energy bordism group vanishes, including type II compactifications on CY3, AdS flux compactifications on 5-manifolds, and M-theory on 7-manifolds. This lends further evidence to the conjecture that any non-supersymmetric vacuum of quantum gravity is ultimately unstable.

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Mechanics of a charged particle on the Kaluza–Klein background

Canadian Journal of Physics ◽

10.1139/p95-087 ◽

1995 ◽

Vol 73 (9-10) ◽

pp. 602-607 ◽

Cited By ~ 2

Author(s):

S. R. Vatsya

Keyword(s):

Electromagnetic Field ◽

Charged Particle ◽

Integral Method ◽

Gordon Equation ◽

Type Equation ◽

Fifth Dimension ◽

Klein Gordon ◽

Path Integral Method ◽

Klein Gordon Equation ◽

Kaluza Klein

The path-integral method is used to derive a generalized Schrödinger-type equation from the Kaluza–Klein Lagrangian for a charged particle in an electromagnetic field. The compactness of the fifth dimension and the properties of the physical paths are used to decompose this equation into its infinite components, one of them being similar to the Klein–Gordon equation.

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BACH FLOWS OF PRODUCT MANIFOLDS

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887812500399 ◽

2012 ◽

Vol 09 (05) ◽

pp. 1250039 ◽

Cited By ~ 2

Author(s):

SANJIT DAS ◽

SAYAN KAR

Keyword(s):

Dynamical System ◽

Fixed Point ◽

Ricci Flow ◽

Flow Characteristics ◽

Geometric Flow ◽

Flow Equations ◽

First Order ◽

Bach Tensor ◽

Point Condition ◽

Future Work

We investigate various aspects of a geometric flow defined using the Bach tensor. First, using a well-known split of the Bach tensor components for (2, 2) unwarped product manifolds, we solve the Bach flow equations for typical examples of product manifolds like S2 × S2, R2 × S2. In addition, we obtain the fixed-point condition for general (2, 2) manifolds and solve it for a restricted case. Next, we consider warped manifolds. For Bach flows on a special class of asymmetrically warped 4-manifolds, we reduce the flow equations to a first-order dynamical system, which is solved exactly to find the flow characteristics. We compare our results for Bach flow with those for Ricci flow and discuss the differences qualitatively. Finally, we conclude by mentioning possible directions for future work.

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