Article
Mathematics
Irfan Glogic
Summary: This paper considers the Yang-Mills equations in (1 + d)-dimensional Minkowski spacetime. It is known that in the supercritical case, i.e., for d >= 5, these equations admit closed form equivariant self-similar blowup solutions. These solutions are conjectured to be the universal attractors for generic large equivariant data evolutions. In this paper, the authors partially prove this conjecture by showing stability of the blowup mechanism exhibited by these solutions for all odd d >= 5.
ADVANCES IN MATHEMATICS
(2022)
Article
Mathematics, Applied
Roland Donninger, Matthias Ostermann
Summary: This paper investigates the Cauchy problem for an energy-supercritical nonlinear wave equation in odd space dimensions that arises in equivariant Yang-Mills theory. It proves the stability of a self-similar finite-time blowup solution under small perturbations of the initial data. The blowup analysis is based on hyperboloidal similarity coordinates and relies crucially on growth estimates for the free wave evolution, which will be constructed systematically for odd space dimensions in the first part of this paper. This allows the development of a nonlinear stability theory beyond the singularity.
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics
Irfan Glogic, Birgit Schorkhuber
Summary: This study focuses on the focusing cubic wave equation and identifies an explicit self-similar blowup solution in all supercritical dimensions. Analyzing stability properties in dimension d = 7 without symmetry assumptions, it proves the existence of perturbations leading to blowup. These perturbations correspond to a co-dimension one Lipschitz manifold in similarity coordinates.
ADVANCES IN MATHEMATICS
(2021)
Article
History & Philosophy Of Science
Adam Koberinski
Summary: This paper details three major mathematical developments that led to the emergence of Yang-Mills theories as the foundation for the standard model of particle physics. By studying historical case studies, lessons for theory construction in physics can be learned, particularly in understanding the consequences and representational capacities of a theoretical framework.
Review
Multidisciplinary Sciences
Roberto Bonezzi, Christoph Chiaffrino, Felipe Diaz-Jaramillo, Olaf Hohm
Summary: This essay justifies its title by discussing a class of Yang-Mills-type theories that include standard Yang-Mills theories and gravity as a double field theory. The framework of homotopy algebras is used, where conventional Yang-Mills theory is represented as the tensor product K circle times g of a 'kinematic' algebra K with a color Lie algebra g. The broader class of Yang-Mills-type theories are given by the tensor product of K with more general Lie-type algebras, including K itself, up to cancelable anomalies when combined with a second copy K over bar. Gravity is then represented by K circle times K over bar.
Article
Physics, Particles & Fields
Fatemeh Naeimipour, Behrouz Mirza, Fatemeh Masoumi Jahromi
Summary: This paper formulates two new classes of black hole solutions in higher curvature quartic quasitopological gravity with nonabelian Yang-Mills theory. The solutions obtained are thermally stable only in the canonical ensemble and may undergo a first order phase transition. Additionally, pure quasitopological Yang-Mills black hole solutions have the ability to produce both AdS and dS black holes for different constant curvatures.
EUROPEAN PHYSICAL JOURNAL C
(2021)
Article
Astronomy & Astrophysics
Alexander D. Popov
Summary: By combining Chern-Simons theory with Twistor space, a complete Yang-Mills theory description can be established on P-6 | 2.
Article
Astronomy & Astrophysics
Mikhail Shifman
Summary: This study focuses on a deformation of pure Yang-Mills theory by a phantom field similar to the Faddeev-Popov ghost, revealing an ersatz supersymmetry that cancels quantum corrections up to two-loop order. By utilizing two complex fields with incorrect statistics, a quadruplet is constructed to balance gauge fields. Furthermore, it is suggested that unitarity of amplitudes persists even in the presence of the phantom, indicating potential broader applications beyond loop calculations.
Article
Physics, Multidisciplinary
Matthias R. Gaberdiel, Rajesh Gopakumar
Summary: In this study, a worldsheet description for the AdS(5) x S-5 string theory was proposed, dual to the large N, free N = 4 supersymmetric Yang-Mills theory. The worldsheet theory is a natural generalization of the tensionless string on AdS(3) x S-3 x T-4, with free field description and spectrally flowed sectors. By imposing a set of residual gauge constraints on the reduced oscillator Fock space, the physical spectrum of the string theory can be determined, reproducing the planar spectrum of single trace operators of the free supersymmetric Yang-Mills theory.
PHYSICAL REVIEW LETTERS
(2021)
Article
Astronomy & Astrophysics
Dmitriy G. Pak, Rong-Gen Cai, Takuya Tsukioka, Pengming Zhang, Yu-Feng Zhou
Summary: We present the basic non-perturbative structure of classical dynamical solutions and one particle quantum states in SU(3) Yang-Mills theory. The Weyl group of su(3) algebra plays a crucial role in constructing these solutions and has profound effects on the structure of the classical and quantum Yang-Mills theory. Our study reveals that the Weyl group allows for singlet irreducible representations on the space of classical dynamical solutions, which provides a strict concept of one particle quantum states for gluons and quarks. We propose a non-perturbative approach based on Weyl symmetric solutions to fully nonlinear equations of motion, resulting in a full space of dynamical solutions classified by a finite set of integer numbers.
Article
Astronomy & Astrophysics
Ouraman Hajizadeh, Markus Q. Huber, Axel Maas, Jan M. Pawlowski
Summary: Reliably computing the free energy in gauge theories like QCD is challenging, but the study shows promising results in obtaining the thermodynamic anomaly from two-point functions. Using advanced techniques and novel results, the research reveals consistent behavior of the gluon propagator at large momentum, encouraging further exploration of this approach for SU(2) Yang-Mills theory.
Article
Mathematics
Roland Donninger, David Wallauch
Summary: In this study, we investigate the stability of corotational wave maps from (1 + 4)-dimensional Minkowski space into the 4-sphere. We prove that a known self-similar wave map remains stable under small perturbations in the critical Sobolev space.
ADVANCES IN MATHEMATICS
(2023)
Article
Mathematics
Goncalo Oliveira, Alex Waldron
Summary: This paper develops Yang-Mills flow on Riemannian manifolds with special holonomy. It is found that a supremum bound on a certain curvature component is sufficient to rule out finite-time singularities, and the infinite-time bubbling set is calibrated by the defining (n-4)-form when such a bound is assumed.
ADVANCES IN MATHEMATICS
(2021)
Article
Physics, Particles & Fields
Danhua Song, Kai Lou, Ke Wu, Jie Yang
Summary: The YM theory has been generalized to 2YM and 3YM theories, and similarly, the BFYM theory has been generalized to 2BFYM and 3BFYM theories. It is shown that these higher BFYM theories can provide formulations for the corresponding higher form YM theories. Additionally, the gauge symmetries of these higher BFYM theories are also studied.
EUROPEAN PHYSICAL JOURNAL C
(2022)
Article
Physics, Particles & Fields
Yifan Wang
Summary: Through the use of supersymmetric localization, it is found that the N = 4 super-Yang-Mills (SYM) theory on unorientable spacetime manifold can be effectively captured by a two-dimensional bosonic Yang-Mills (YM) theory. This provides a foundation for understanding the relationship between the two theories.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
