scholarly journals Small instantons in weakly-gauged holographic models

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Tony Gherghetta ◽  
Alex Pomarol
Keyword(s):  
Topological Charge ◽  
Conformal Transformation ◽  
Analytic Solutions ◽  
Strongly Coupled ◽  
Yang Mills ◽  
Interesting Class ◽  
Gauge Couplings ◽  
Topological Charges

Abstract Small instantons can play an important role in Yang-Mills theories whose gauge couplings are sizeable at small distances. An interesting class of theories where this could occur is in weakly-gauged holographic models (dual to Yang-Mills theories interacting with strongly-coupled CFTs), since gauge couplings are indeed enhanced towards the UV boundary of the 5D AdS space. However, contrary to expectations, we show that small instantons in these non-asymptotically-free models are highly suppressed and ineffective. This is due to the conservation of topological charge that forbids instantons to be localized near the UV boundary. Despite this fact we find non-trivial UV localized instanton-anti-instanton solutions of the Yang-Mills equations where the topological charges annihilate in the AdS bulk. These analytic solutions arise from a 5D conformal transformation of the uplifted 4D instanton. Our analysis therefore reveals unexpected nonperturbative configurations of Yang-Mills theories when they interact with strongly-coupled CFTs.

scholarly journals Non-linear composition and infinite conformal symmetry of topologically non-trivial solutions in $$(3+1)$$-dimensional Yang–Mills theory

2021 ◽  
Vol 81 (11) ◽  
Author(s):  
Fabrizio Canfora
Keyword(s):  
Scalar Field ◽  
Charge Density ◽  
Topological Charge ◽  
Conformal Symmetry ◽  
Analytic Solutions ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Field Equations ◽  
Yang Mills ◽  
Non Linear

AbstractAn infinite-dimensional family of analytic solutions in pure SU(2) Yang–Mills theory at finite density in $$(3+1)$$ ( 3 + 1 ) dimensions is constructed. It is labelled by two integeres (p and q) as well as by a two-dimensional free massless scalar field. The gauge field depends on all the 4 coordinates (to keep alive the topological charge) but in such a way to reduce the (3+1)-dimensional Yang–Mills field equations to the field equation of a 2D free massless scalar field. For each p and q, both the on-shell action and the energy-density reduce to the action and Hamiltonian of the corresponding 2D CFT. The topological charge density associated to the non-Abelian Chern–Simons current is non-zero. It is possible to define a non-linear composition within this family as if these configurations were “Lego blocks”. The non-linear effects of Yang–Mills theory manifest themselves since the topological charge density of the composition of two solutions is not the sum of the charge densities of the components. This leads to an upper bound on the amplitudes in order for the topological charge density to be well-defined. This suggests that if the temperature and/or the energy is/are high enough, the topological density of these configurations is not well-defined anymore. Semiclassically, one can show that (depending on whether the topological charge is even or odd) some of the operators appearing in the 2D CFT should be quantized as Fermions (despite the Bosonic nature of the classical field).

scholarly journals Strongly coupled QFT dynamics via TQFT coupling

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Mithat Ünsal
Keyword(s):  
Strong Coupling ◽  
Topological Charge ◽  
Background Field ◽  
Strong Coupling Regime ◽  
Global Symmetry ◽  
Quantum Field Theories ◽  
Strongly Coupled ◽  
Yang Mills ◽  
Mass Gap ◽  
New Perspective

Abstract We consider a class of quantum field theories and quantum mechanics, which we couple to ℤN topological QFTs, in order to classify non-perturbative effects in the original theory. The ℤN TQFT structure arises naturally from turning on a classical background field for a ℤN 0- or 1-form global symmetry. In SU(N) Yang-Mills theory coupled to ℤN TQFT, the non-perturbative expansion parameter is exp[−SI/N] = exp[−8π2/g2N] both in the semi-classical weak coupling domain and strong coupling domain, corresponding to a fractional topological charge configurations. To classify the non-perturbative effects in original SU(N) theory, we must use PSU(N) bundle and lift configurations (critical points at infinity) for which there is no obstruction back to SU(N). These provide a refinement of instanton sums: integer topological charge, but crucially fractional action configurations contribute, providing a TQFT protected generalization of resurgent semi-classical expansion to strong coupling. Monopole-instantons (or fractional instantons) on T3 × $$ {S}_L^1 $$ S L 1 can be interpreted as tunneling events in the ’t Hooft flux background in the PSU(N) bundle. The construction provides a new perspective to the strong coupling regime of QFTs and resolves a number of old standing issues, especially, fixes the conflicts between the large-N and instanton analysis. We derive the mass gap at θ = 0 and gaplessness at θ = π in $$ \mathbbm{CP} $$ CP 1 model, and mass gap for arbitrary θ in $$ \mathbbm{CP} $$ CP N−1, N ≥ 3 on ℝ2.

scholarly journals Yang–Mills instanton sheaves with higher topological charges

2019 ◽  
Vol 16 (07) ◽  
pp. 1950112 ◽  
Author(s):  
Sheng-Hong Lai ◽  
Jen-Chi Lee ◽  
I-Hsun Tsai
Keyword(s):  
Topological Charge ◽  
Yang Mills ◽  
Topological Charges

We explicitly construct [Formula: see text] (or [Formula: see text] complex) Yang–Mills (YM) (weakly) three and four instanton sheaves on [Formula: see text]. These results extend the previous construction of YM (weakly) instanton sheaves with topological charge two [S. H. Lai, J. C. Lee and I. H. Tsai, Yang–Mills instanton sheaves, Ann. Phys. 377 (2017) 446, arXiv:1603.02860 ].

scholarly journals Effect of Deformation on Topological Properties of Cobalt Monosilicide

Crystals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 143
Author(s):  
Sergey Nikolaev ◽  
Dmitry Pshenay-Severin ◽  
Yuri Ivanov ◽  
Alexander Burkov
Keyword(s):  
Band Structure ◽  
Ab Initio Calculations ◽  
Topological Charge ◽  
External Stress ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Topological Properties ◽  
Uniaxial Deformation ◽  
Band Crossing ◽  
Topological Charges

Recently, it was shown that materials with certain crystal structures can exhibit multifold band crossings with large topological charges. CoSi is one such material that belongs to non-centrosymmetric space group P213 (#198) and posseses multifold band crossing points with a topological charge of 4. The change of crystal symmetry, e.g., by means of external stress, can lift the degeneracy and change its topological properties. In the present work, the influence of uniaxial deformation on the band structure and topological properties of CoSi is investigated on the base of ab initio calculations. The k·p Hamiltonian taking into account deformation is constructed on the base of symmetry consideration near the Γ and R points both with and without spin-orbit coupling. The transformation of multifold band crossings into nodes of other types with different topological charges, their shift both in energy and in reciprocal space and the tilt of dispersion around nodes are studied in detail depending on the direction of uniaxial deformation.

scholarly journals High-Efficiency Spin-Related Vortex Metalenses

Nanomaterials ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 1485
Author(s):  
Wei Wang ◽  
Ruikang Zhao ◽  
Shilong Chang ◽  
Jing Li ◽  
Yan Shi ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Topological Charge ◽  
High Efficiency ◽  
Infrared Band ◽  
Mid Infrared ◽  
Integrated Devices ◽  
Vortex Beams ◽  
Topological Charges

In this paper, one spin-selected vortex metalens composed of silicon nanobricks is designed and numerically investigated at the mid-infrared band, which can produce vortex beams with different topological charges and achieve different spin lights simultaneously. Another type of spin-independent vortex metalens is also designed, which can focus the vortex beams with the same topological charge at the same position for different spin lights, respectively. Both of the two vortex metalenses can achieve high-efficiency focusing for different spin lights. In addition, the spin-to-orbital angular momentum conversion through the vortex metalens is also discussed in detail. Our work facilitates the establishment of high-efficiency spin-related integrated devices, which is significant for the development of vortex optics and spin optics.

FINITE ENERGY ONE-HALF MONOPOLE SOLUTIONS

2012 ◽  
Vol 27 (40) ◽  
pp. 1250233 ◽  
Author(s):  
ROSY TEH ◽  
BAN-LOONG NG ◽  
KHAI-MING WONG
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Magnetic Flux ◽  
Topological Charge ◽  
Magnetic Monopole ◽  
Magnetic Charge ◽  
Finite Energy ◽  
Spatial Infinity ◽  
Yang Mills ◽  
The Magnetic Field

We present finite energy SU(2) Yang–Mills–Higgs particles of one-half topological charge. The magnetic fields of these solutions at spatial infinity correspond to the magnetic field of a positive one-half magnetic monopole at the origin and a semi-infinite Dirac string on one-half of the z-axis carrying a magnetic flux of [Formula: see text] going into the origin. Hence the net magnetic charge is zero. The gauge potentials are singular along one-half of the z-axis, elsewhere they are regular.

scholarly journals Higgsing towards E-strings

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Joonho Kim ◽  
Seok Kim ◽  
Kimyeong Lee
Keyword(s):  
String Theory ◽  
Gauge Theories ◽  
The Self ◽  
Flavor Symmetry ◽  
Strongly Coupled ◽  
Superconformal Field Theories ◽  
Yang Mills ◽  
Gauge Symmetries ◽  
Elliptic Genera ◽  
Linear Sigma Models

Abstract We explore 6d (1, 0) superconformal field theories with SU(3) and SU(2) gauge symmetries which cascade after Higgsing to the E-string theory on a single M5 near an E8 wall. Specifically, we study the 2d $$ \mathcal{N} $$ N = (0, 4) gauge theories which describe self-dual strings of these 6d theories. The self-dual strings can be also viewed as instanton string solitons of 6d Yang-Mills theories. We find the 2d anomaly-free gauge theories for self-dual strings, amending the naive ADHM gauge theories which are anomalous, and calculate their elliptic genera. While these 2d theories respect the flavor symmetry of each 6d SCFT only partially, their elliptic genera manifest the symmetry fully as these functions as BPS index are invariant in strongly coupled IR limit. Our consistent 2d (0, 4) gauge theories also provide new insights on the non-linear sigma models for the instanton strings, providing novel UV completions of the small instanton singularities. Finally, we construct new 2d quiver gauge theories for the self-dual strings in 6d E-string theory for multiple M5-branes probing the E8 wall, and find their fully refined elliptic genera.

scholarly journals Screening in strongly coupled $ \mathcal{N} = {2^*} $ supersymmetric Yang-Mills plasma

2011 ◽  
Vol 2011 (10) ◽  
Author(s):  
Carlos Hoyos ◽  
Steve Paik ◽  
Laurence G. Yaffe
Keyword(s):  
Strongly Coupled ◽  
Yang Mills

scholarly journals Diluted mass gap in strongly coupled non-local Yang-Mills

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Marco Frasca ◽  
Anish Ghoshal
Keyword(s):  
Field Theory ◽  
Particle Physics ◽  
Mass Scale ◽  
Local Theory ◽  
Quantum Field ◽  
Strongly Coupled ◽  
Yang Mills ◽  
Mass Gap ◽  
Non Local ◽  
Non Locality

Abstract We investigate the non-perturbative regimes in the class of non-Abelian theories that have been proposed as an ultraviolet completion of 4-D Quantum Field Theory (QFT) generalizing the kinetic energy operators to an infinite series of higher-order derivatives inspired by string field theory. We prove that, at the non-perturbative level, the physical spectrum of the theory is actually corrected by the “infinite number of derivatives” present in the action. We derive a set of Dyson-Schwinger equations in differential form, for correlation functions till two-points, the solution for which are known in the local theory. We obtain that just like in the local theory, the non-local counterpart displays a mass gap, depending also on the mass scale of non-locality, and show that it is damped in the deep UV asymptotically. We point out some possible implications of our result in particle physics and cosmology and discuss aspects of non-local QCD-like scenarios.

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