scholarly journals EMERGENCE OF TIME FROM DIMENSIONAL REDUCTION IN NONCOMMUTATIVE GEOMETRY

2006 ◽  
Vol 21 (08) ◽  
pp. 639-647 ◽  
Author(s):  
CHONG-SUN CHU ◽  
OLAF LECHTENFELD
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Noncommutative Geometry ◽  
Dimensional Reduction ◽  
Euclidean Geometry ◽  
Noncommutative Field Theory ◽  
Fundamental Theory ◽  
Temporal Dimension ◽  
New Form

By considering a new form of dimensional reduction for noncommutative field theory, we show that the signature of spacetime may be changed. In particular, it is demonstrated that a temporal dimension can emerge from a purely Euclidean geometry. We suggest that this mechanism may hint at the origin of time in the fundamental theory of quantum gravity.

scholarly journals LOCALITY, CAUSALITY AND NONCOMMUTATIVE GEOMETRY

2006 ◽  
Vol 21 (01) ◽  
pp. 67-82 ◽  
Author(s):  
CHONG-SUN CHU ◽  
KO FURUTA ◽  
TAKEO INAMI
Keyword(s):  
Field Theory ◽  
Noncommutative Geometry ◽  
Light Cone ◽  
Energy Condition ◽  
Noncommutative Space ◽  
Noncommutative Field Theory ◽  
Causality Condition ◽  
Usual Form ◽  
New Form ◽  
Lower Dimensional

We analyze the causality condition in noncommutative field theory and show that the nonlocality of noncommutative interaction leads to a modification of the light cone to the light wedge. This effect is generic for noncommutative geometry. We also check that the usual form of energy condition is violated and propose that a new form is needed in noncommutative space–time. On reduction from light cone to light wedge, it looks like the noncommutative dimensions are effectively washed out and suggests a reformulation of noncommutative field theory in terms of lower dimensional degree of freedom. This reduction of dimensions due to noncommutative geometry could play a key role in explaining the holographic property of quantum gravity.

scholarly journals Nonlinear connections and spinor geometry

2004 ◽  
Vol 2004 (23) ◽  
pp. 1189-1237 ◽  
Author(s):  
Sergiu I. Vacaru ◽  
Nadejda A. Vicol
Keyword(s):  
Field Theory ◽  
Noncommutative Geometry ◽  
Finsler Geometry ◽  
Higher Order ◽  
Noncommutative Field Theory ◽  
Local Anisotropy ◽  
Nonlinear Connection ◽  
Nonlinear Connections ◽  
Spinor Geometry ◽  
Kaluza Klein

We present an introduction to the geometry of higher-order vector and covector bundles (including higher-order generalizations of the Finsler geometry and Kaluza-Klein gravity) and review the basic results on Clifford and spinor structures on spaces with generic local anisotropy modeled by anholonomic frames with associated nonlinear connection structures. We emphasize strong arguments for application of Finsler-like geometries in modern string and gravity theory, noncommutative geometry and noncommutative field theory, and gravity.

scholarly journals D-BRANES, CYCLIC SYMMETRY AND NONCOMMUTATIVE GEOMETRY

2003 ◽  
Vol 18 (15) ◽  
pp. 1053-1065 ◽  
Author(s):  
SUPRIYA KAR
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Noncommutative Geometry ◽  
Open String ◽  
Cyclic Symmetry ◽  
Noncommutative Field Theory ◽  
World Volume ◽  
The World ◽  
Point Splitting

In this paper, we study the open string modes, describing the world-volume of a D p-brane, for its cyclic symmetry in the presence of a magnetic field. We outline the analogy between cyclic and noncommutative symmetries and demonstrate the point-splitting prescription to explain some of the unusual ir phenomena observed in a noncommutative field theory.

scholarly journals ELIMINATION OF IR/UV VIA GRAVITY IN NONCOMMUTATIVE FIELD THEORY

2008 ◽  
Vol 23 (39) ◽  
pp. 3341-3348 ◽  
Author(s):  
N. KERSTING ◽  
J. YAN
Keyword(s):  
Field Theory ◽  
Noncommutative Geometry ◽  
Particle Physics ◽  
Degrees Of Freedom ◽  
Noncommutative Field Theory

Models of particle physics with Noncommutative Geometry (NCG) generally suffer from a manifestly non-Wilsonian coupling of infrared and ultraviolet degrees of freedom known as the "IR/UV Problem" which would tend to compromise their phenomenological relevance. In this letter we explicitly show how one may remedy this by coupling NCG to gravity. In the simplest scenario, the Lagrangian gets multiplied by a nonconstant background metric; in ϕ-4 theory the theorem that ∫ d4x ϕ⋆ϕ=∫ d4x ϕ2 is no longer true and the field propagator gets modified by a factor which depends on both NCG and the variation of the metric. A suitable limit of this factor as the propagating momentum gets asymptotically large then eradicates the IR/UV problem. With gravity and NCG coupled to each other, one might expect antisymmetric components to arise in the metric. Cosmological implications of such are subsequently discussed.

scholarly journals Non-Riemannian gravity actions from double field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
A. D. Gallegos ◽  
U. Gürsoy ◽  
S. Verma ◽  
N. Zinnato
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Condensed Matter ◽  
Equations Of Motion ◽  
Technical Note ◽  
Action Principle ◽  
Relativistic Symmetry ◽  
Gravitational Theories ◽  
Double Field Theory

Abstract Non-Riemannian gravitational theories suggest alternative avenues to understand properties of quantum gravity and provide a concrete setting to study condensed matter systems with non-relativistic symmetry. Derivation of an action principle for these theories generally proved challenging for various reasons. In this technical note, we employ the formulation of double field theory to construct actions for a variety of such theories. This formulation helps removing ambiguities in the corresponding equations of motion. In particular, we embed Torsional Newton-Cartan gravity, Carrollian gravity and String Newton-Cartan gravity in double field theory, derive their actions and compare with the previously obtained results in literature.

scholarly journals Singularity Theorems in the Effective Field Theory for Quantum Gravity at Second Order in Curvature

Universe ◽  
2020 ◽  
Vol 6 (10) ◽  
pp. 171
Author(s):  
Folkert Kuipers ◽  
Xavier Calmet
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Effective Field Theory ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Effective Field ◽  
Second Order ◽  
Jordan Frame ◽  
Singularity Theorems ◽  
Massive Spin

In this paper, we discuss singularity theorems in quantum gravity using effective field theory methods. To second order in curvature, the effective field theory contains two new degrees of freedom which have important implications for the derivation of these theorems: a massive spin-2 field and a massive spin-0 field. Using an explicit mapping of this theory from the Jordan frame to the Einstein frame, we show that the massive spin-2 field violates the null energy condition, while the massive spin-0 field satisfies the null energy condition, but may violate the strong energy condition. Due to this violation, classical singularity theorems are no longer applicable, indicating that singularities can be avoided, if the leading quantum corrections are taken into account.

scholarly journals Quantum channels in quantum gravity

2014 ◽  
Vol 23 (12) ◽  
pp. 1442009 ◽  
Author(s):  
Mukund Rangamani ◽  
Massimilliano Rota
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Quantum Gravity ◽  
Path Integrals ◽  
Quantum Channels ◽  
Hole Formation ◽  
Integral Formalism ◽  
Final State ◽  
State Boundary ◽  
Gauge Gravity

The black hole final state proposal implements manifest unitarity in the process of black hole formation and evaporation in quantum gravity, by postulating a unique final state boundary condition at the singularity. We argue that this proposal can be embedded in the gauge/gravity context by invoking a path integral formalism inspired by the Schwinger–Keldysh like thermo-field double construction in the dual field theory. This allows us to realize the gravitational quantum channels for information retrieval to specific deformations of the field theory path integrals and opens up new connections between geometry and information theory.

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