scholarly journals THE GAUGE DUAL OF GAUGED ${\mathcal N}=8$ SUPERGRAVITY THEORY

2010 ◽  
Vol 25 (15) ◽  
pp. 3025-3041 ◽  
Author(s):  
CHANGHYUN AHN
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Scalar Fields ◽  
Three Dimensions ◽  
Supergravity Theory ◽  
Arbitrary Mass ◽  
Four Dimensions

The most general SU(3) -singlet space of gauged [Formula: see text] supergravity in four-dimensions is studied recently. The SU(3) -invariant six scalar fields are realized by six real four-forms. A family of holographic [Formula: see text] supersymmetric RG flows on M2-branes in three-dimensions is described. This family of flows is driven by three independent mass parameters from the [Formula: see text] theory and is controlled by two IR fixed points, [Formula: see text]-invariant one and [Formula: see text]-invariant one. The generic flow with arbitrary mass parameters is [Formula: see text] supersymmetric and reaches to the [Formula: see text] fixed point where the three masses become identical. A particular [Formula: see text] supersymmetric SU(3) -preserving RG flow from the [Formula: see text]-invariant fixed point to the [Formula: see text]-invariant fixed point is also discussed.

Large-momentum behaviour in quantum field theory (QFT)

2021 ◽  
pp. 593-606
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Fixed Point ◽  
Fixed Points ◽  
Quantum Electrodynamics ◽  
Particle Physics ◽  
Large Momentum ◽  
Quantum Field ◽  
Four Dimensions ◽  
Free Theory ◽  
Electron Positron Annihilation

Renormalization group (RG) equations are used to characterize the large momentum behaviour of renormalized quantum field theories (QFT), assuming implicitly that such a universal large momentum physics can be defined, something which, beyond perturbation theory is not obvious. Since the initial effective QFT is valid only up to an energy-momentum scale much smaller than some cut-off, large momentum means much larger than the renormalization scale, but still much smaller than the cut-off scale. The existence of this large momentum physics implies the existence of a crossover scale between low and large momentum physics. One theoretic reason for discussing the large momentum behaviour is the apparent connection between the existence of consistent interacting renormalized QFTs and the presence of ultraviolet (UV) fixed points. The absence of identified UV fixed points in infrared-free QFTs, like the φ4 field theory or quantum electrodynamics (QED), leads to the triviality issue. The physics reason is that in collisions it is observed that quarks, fundamental particles of the Standard Model (SM) of particle physics, behave like free particles at the shortest distances presently accessible (the property of asymptotic freedom). This property can be explained by RG arguments if the free theory is an attractive UV fixed point. Therefore, the identification of QFTs where the free theory is an UV fixed point is important, and this has led to examine the large momentum behaviour of all QFTs renormalizable in four dimensions. It is shown that only theories having a non-Abelian gauge symmetry can be asymptotically free. As an application, the total cross section of electron–positron annihilation into hadrons at large momentum is calculated.

scholarly journals FLOW OF THE COARSE GRAINED FREE ENERGY FOR CROSSOVER PHENOMENA

1999 ◽  
Vol 14 (06) ◽  
pp. 899-918 ◽  
Author(s):  
S. BORNHOLDT ◽  
P. BÜTTNER ◽  
N. TETRADIS ◽  
C. WETTERICH
Keyword(s):  
Free Energy ◽  
Fixed Points ◽  
Critical Behavior ◽  
Scalar Fields ◽  
Three Dimensions ◽  
Coarse Grained ◽  
Average Action

The critical behavior of a system of two coupled scalar fields in three dimensions is studied within the formalism of the effective average action. The fixed points of the system are identified and the crossover between them is described in detail. Besides the universal critical behavior, the flow of the coarse grained free energy also describes the approach to scaling.

scholarly journals SUPERGRAVITY IN 2+∊ DIMENSIONS

1994 ◽  
Vol 09 (31) ◽  
pp. 5415-5444 ◽  
Author(s):  
SHIN-ICHI KOJIMA ◽  
NORISUKE SAKAI ◽  
YOSHIAKI TANII
Keyword(s):  
Fixed Point ◽  
Dimensional Reduction ◽  
Background Field ◽  
Field Method ◽  
Three Dimensions ◽  
Supergravity Theory ◽  
Anomalous Dimensions ◽  
Gauge Fixing ◽  
Background Field Method

Supergravity theory in 2+∊ dimensions is studied. It is invariant under supertransformations in two and three dimensions. One-loop divergence is explicitly computed by the background field method and a nontrivial fixed point is found. In quantizing the supergravity, a gauge-fixing condition is devised which explicitly isolates conformal and superconformal modes. The renormalization of the gravitationally dressed operators is studied and their anomalous dimensions are computed. Problems in using the dimensional reduction are also examined.

scholarly journals Bounds on multiscalar CFTs in the ε expansion

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Matthijs Hogervorst ◽  
Chiara Toldo
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Scalar Fields ◽  
Final Part ◽  
Leading Order ◽  
Quartic Coupling ◽  
Specific Domain ◽  
Bottom Up ◽  
Anomalous Dimensions ◽  
Do So

Abstract We study fixed points with N scalar fields in 4 − ε dimensions to leading order in ε using a bottom-up approach. We do so by analyzing O(N) invariants of the quartic coupling λijkl that describes such CFTs. In particular, we show that λiijj and $$ {\lambda}_{ijkl}^2 $$ λ ijkl 2 are restricted to a specific domain, refining a result by Rychkov and Stergiou. We also study averages of one-loop anomalous dimensions of composite operators without gradients. In many cases, we are able to show that the O(N) fixed point maximizes such averages. In the final part of this work, we generalize our results to theories with N complex scalars and to bosonic QED. In particular we show that to leading order in ε, there are no bosonic QED fixed points with N < 183 flavors.

A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3157-3172
Author(s):  
Mujahid Abbas ◽  
Bahru Leyew ◽  
Safeer Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Metric Space ◽  
Delay Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

scholarly journals New AdS4 vacua in dyonic ISO(7) gauged supergravity

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Nikolay Bobev ◽  
Thomas Fischbacher ◽  
Fridrik Freyr Gautason ◽  
Krzysztof Pilch
Keyword(s):  
Scalar Fields ◽  
Global Symmetry ◽  
Supergravity Theory

Abstract We identify 219 AdS4 solutions in four-dimensional dyonically gauged ISO(7) $$ \mathcal{N} $$ N = 8 supergravity and present some of their properties. One of the new solutions preserves $$ \mathcal{N} $$ N = 1 supersymmetry and provides a rare explicit example of an AdS4 vacuum dual to a 3d SCFT with no continuous global symmetry. There are also two new non-supersymmetric solutions for which all 70 scalar fields in the supergravity theory have masses above the BF bound. All of these AdS4 solutions can be uplifted to massive type IIA supergravity. Motivated by this we present the low lying operator spectra of the dual 3d CFTs for all known supersymmetric AdS4 solutions in the theory and organize them into superconformal multiplets.

Coincidence and fixed points for hybrid tangential maps

2010 ◽  
Vol 17 (2) ◽  
pp. 273-285
Author(s):  
Tayyab Kamran ◽  
Quanita Kiran
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Property ◽  
Fixed Point Theorems ◽  
Acta Math ◽  
Contractive Condition ◽  
The Common

Abstract In [Int. J. Math. Math. Sci. 2005: 3045–3055] by Liu et al. the common property (E.A) for two pairs of hybrid maps is defined. Recently, O'Regan and Shahzad [Acta Math. Sin. (Engl. Ser.) 23: 1601–1610, 2007] have introduced a very general contractive condition and obtained some fixed point results for hybrid maps. We introduce a new property for pairs of hybrid maps that contains the property (E.A) and obtain some coincidence and fixed point theorems that extend/generalize some results from the above-mentioned papers.

scholarly journals Solution of Some Impulsive Differential Equations via Coupled Fixed Point

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 501
Author(s):  
Ahmed Boudaoui ◽  
Khadidja Mebarki ◽  
Wasfi Shatanawi ◽  
Kamaleldin Abodayeh
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
System Of Differential Equations ◽  
Coupled Fixed Points

In this article, we employ the notion of coupled fixed points on a complete b-metric space endowed with a graph to give sufficient conditions to guarantee a solution of system of differential equations with impulse effects. We derive recisely some new coupled fixed point theorems under some conditions and then apply our results to achieve our goal.

scholarly journals Symmetry breaking at high temperatures in large N gauge theories

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Soumyadeep Chaudhuri ◽  
Eliezer Rabinovici
Keyword(s):  
Fixed Point ◽  
Phase Transitions ◽  
Symmetry Breaking ◽  
High Temperatures ◽  
Gauge Theories ◽  
Scalar Fields ◽  
Temperature Limit ◽  
Spontaneous Breaking ◽  
Critical Temperatures ◽  
Weakly Coupled

Abstract Considering marginally relevant and relevant deformations of the weakly coupled (3 + 1)-dimensional large N conformal gauge theories introduced in [1], we study the patterns of phase transitions in these systems that lead to a symmetry-broken phase in the high temperature limit. These deformations involve only the scalar fields in the models. The marginally relevant deformations are obtained by varying certain double trace quartic couplings between the scalar fields. The relevant deformations, on the other hand, are obtained by adding masses to the scalar fields while keeping all the couplings frozen at their fixed point values. At the N → ∞ limit, the RG flows triggered by these deformations approach the aforementioned weakly coupled CFTs in the UV regime. These UV fixed points lie on a conformal manifold with the shape of a circle in the space of couplings. As shown in [1], in certain parameter regimes a subset of points on this manifold exhibits thermal order characterized by the spontaneous breaking of a global ℤ2 or U(1) symmetry and Higgsing of a subset of gauge bosons at all nonzero temperatures. We show that the RG flows triggered by the marginally relevant deformations lead to a weakly coupled IR fixed point which lacks the thermal order. Thus, the systems defined by these RG flows undergo a transition from a disordered phase at low temperatures to an ordered phase at high temperatures. This provides examples of both inverse symmetry breaking and symmetry nonrestoration. For the relevant deformations, we demonstrate that a variety of phase transitions are possible depending on the signs and magnitudes of the squares of the masses added to the scalar fields. Using thermal perturbation theory, we derive the approximate values of the critical temperatures for all these phase transitions. All the results are obtained at the N → ∞ limit. Most of them are found in a reliable weak coupling regime and for others we present qualitative arguments.

scholarly journals LARGE QUANTUM GRAVITY EFFECTS: CYLINDRICAL WAVES IN FOUR DIMENSIONS

2000 ◽  
Vol 09 (06) ◽  
pp. 669-686 ◽  
Author(s):  
MARÍA E. ANGULO ◽  
GUILLERMO A. MENA MARUGÁN
Keyword(s):  
Quantum Gravity ◽  
Symmetry Axis ◽  
Point Of View ◽  
Three Dimensions ◽  
Asymptotic Region ◽  
Four Dimensions ◽  
Cylindrical Waves ◽  
Significant Difference ◽  
Gravity Effects ◽  
Linearly Polarized

Linearly polarized cylindrical waves in four-dimensional vacuum gravity are mathematically equivalent to rotationally symmetric gravity coupled to a Maxwell (or Klein–Gordon) field in three dimensions. The quantization of this latter system was performed by Ashtekar and Pierri in a recent work. Employing that quantization, we obtain here a complete quantum theory which describes the four-dimensional geometry of the Einstein–Rosen waves. In particular, we construct regularized operators to represent the metric. It is shown that the results achieved by Ashtekar about the existence of important quantum gravity effects in the Einstein–Maxwell system at large distances from the symmetry axis continue to be valid from a four-dimensional point of view. The only significant difference is that, in order to admit an approximate classical description in the asymptotic region, states that are coherent in the Maxwell field need not contain a large number of photons anymore. We also analyze the metric fluctuations on the symmetry axis and argue that they are generally relevant for all of the coherent states.

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