Yang-Mills Research Articles

Einstein–Yang–Mills Wormholes Haunted by a Phantom Field

In this article, we study wormhole spacetimes in the framework of the static spherically symmetric SU(2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extbf {SU}} (2)$$\\end{document} Einstein–Yang–Mills theory coupled to a phantom scalar field. We show rigorously the existence of an infinite sequence of symmetric wormhole solutions, labelled by the number of zeros of the Yang–Mills potential. These solutions have previously been discovered numerically. Mathematically, the problem resembles the pure Einstein–Yang–Mills system for black hole initial conditions, which was well-studied in the 90s. The main difference in the present work is that the coupling to the phantom field adds a non-trivial degree of complexity to the analysis. After proving the existence of the symmetric wormhole solutions, we also present numerical evidence for the existence of asymmetric ones.

A cluster of results on amplituhedron tiles

The amplituhedron is a mathematical object which was introduced to provide a geometric origin of scattering amplitudes in N=4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {N}=4$$\\end{document} super Yang–Mills theory. It generalizes cyclic polytopes and the positive Grassmannian and has a very rich combinatorics with connections to cluster algebras. In this article, we provide a series of results about tiles and tilings of the m=4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m=4$$\\end{document} amplituhedron. Firstly, we provide a full characterization of facets of BCFW tiles in terms of cluster variables for Gr4,n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext{ Gr}_{4,n}$$\\end{document}. Secondly, we exhibit a tiling of the m=4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m=4$$\\end{document} amplituhedron which involves a tile which does not come from the BCFW recurrence—the spurion tile, which also satisfies all cluster properties. Finally, strengthening the connection with cluster algebras, we show that each standard BCFW tile is the positive part of a cluster variety, which allows us to compute the canonical form of each such tile explicitly in terms of cluster variables for Gr4,n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext{ Gr}_{4,n}$$\\end{document}. This paper is a companion to our previous paper “Cluster algebras and tilings for the m=4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m=4$$\\end{document} amplituhedron.”

Interpolating gauge-fixing for Yang–Mills–Chern–Simons theory in D=3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D=3$$\\end{document}

The Yang–Mills–Chern–Simons theory in three-dimensional Minkowski space-time is studied in a gauge-fixing scheme which interpolates between the covariant gauge and light-cone gauge, the interpolating gauge-fixing. The ultraviolet finiteness of the theory is proved via the Becchi–Rouet–Stora (BRS) algebraic renormalization procedure, which allows us to demonstrate the vanishing of all β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}-functions and all anomalous dimensions to all orders in perturbation theory.

Baryon junction and string interactions

We study junctions between confining strings. We show that the effective theory of such junctions is very predictive, with only one new parameter, the junction’s mass, controlling the first couple of terms in the expansion in the system size. By open-closed string duality, these considerations about the baryon junction map to interaction vertices of closed strings. Therefore, we calculate the interaction vertices of closed strings in theories such as Yang-Mills theory. We find some surprising selection rules for string interactions in 3+1 dimensions. Requiring perturbative stability and that the string coupling is weak, we suggest constraints on the junction’s mass. Published by the American Physical Society 2024

Quantum Simulation of SU(3) Lattice Yang-Mills Theory at Leading Order in Large-N_{c} Expansion.

Quantum simulations of the dynamics of QCD have been limited by the complexities of mapping the continuous gauge fields onto quantum computers. By parametrizing the gauge invariant Hilbert space in terms of plaquette degrees of freedom, we show how the Hilbert space and interactions can be expanded in inverse powers of N_{c}. At leading order in this expansion, the Hamiltonian simplifies dramatically, both in the required size of the Hilbert space as well as the type of interactions involved. Adding a truncation of the resulting Hilbert space in terms of local energy states we give explicit constructions that allow simple representations of SU(3) gauge fields on qubits and qutrits. This formulation allows a simulation of the real time dynamics of a SU(3) lattice gauge theory on a 5×5 and 8×8 lattice on ibm_torino with a CNOT depth of 113.

The Dirac–Higgs Complex and Categorification of (BBB)-Branes

Abstract Let ${\mathcal{M}}_{\operatorname{Dol}}(X,G)$ denote the hyperkähler moduli space of $G$-Higgs bundles over a smooth projective curve $X$. In the context of four dimensional supersymmetric Yang–Mills theory, Kapustin and Witten introduced the notion of (BBB)-brane: boundary conditions that are compatible with the B-model twist in every complex structure of ${\mathcal{M}}_{\operatorname{Dol}}(X,G)$. The geometry of such branes was initially proposed to be hyperkähler submanifolds that support a hyperholomorphic bundle. Gaiotto has suggested a more general type of (BBB)-brane defined by perfect analytic complexes on the Deligne–Hitchin twistor space $\operatorname{Tw}({\mathcal{M}}_{\operatorname{Dol}}(X,G))$. Following Gaiotto’s suggestion, this paper proposes a framework for the categorification of (BBB)-branes, both on the moduli spaces and on the corresponding derived moduli stacks. We do so by introducing the Deligne stack, a derived analytic stack with corresponding moduli space $\operatorname{Tw}({\mathcal{M}}_{\operatorname{Dol}}(X,G))$, defined as a gluing between two analytic Hodge stacks along the Riemann–Hilbert correspondence. We then construct a class of (BBB)-branes using integral functors that arise from higher non-abelian Hodge theory, before discussing their relation to the Wilson functors from the Dolbeault geometric Langlands correspondence.

The Yang–Mills–Higgs functional on complex line bundles: Asymptotics for critical points

Abstract We consider a gauge-invariant Ginzburg–Landau functional (also known as Abelian Yang–Mills–Higgs model), on Hermitian line bundles over closed Riemannian manifolds of dimension n ≥ 3 {n\geq 3} . Assuming a logarithmic energy bound in the coupling parameter, we study the asymptotic behaviour of critical points in the London limit. After a convenient choice of the gauge, we show compactness of finite-energy critical points in Sobolev norms. Moreover, thanks to a suitable monotonicity formula, we prove that the energy densities of critical points, rescaled by the logarithm of the coupling parameter, converge to the weight measure of a stationary, rectifiable varifold of codimension 2.

Transforming the bootstrap: using transformers to compute scattering amplitudes in planar N=4 super Yang–Mills theory

Abstract We pursue the use of deep learning methods to improve state-of-the-art computations in theoretical high-energy physics. Planar N = 4 Super Yang-Mills theory is a close cousin to the theory that describes Higgs boson production at the Large Hadron Collider; its scattering amplitudes are large mathematical expressions containing integer coefficients. In this paper, we apply Transformers to predict these coefficients. The problem can be formulated in a language-like representation amenable to standard cross-entropy training objectives. We design two related experiments and show that the model achieves high accuracy (> 98%) on both tasks. Our work shows that Transformers can be applied successfully to problems in theoretical physics that require exact solutions.

Retrieving Yang–Mills–Higgs fields in Minkowski space from active local measurements

Retrieving Yang–Mills–Higgs fields in Minkowski space from active local measurements

Full QCD with milder topological freezing

We simulate Nf = 2 + 1 QCD at the physical point combining open and periodic boundary conditions in a parallel tempering framework, following the original proposal by M. Hasenbusch for 2d CPN−1 models, which has been recently implemented and widely employed in 4d SU(N) pure Yang-Mills theories too. We show that using this algorithm it is possible to achieve a sizable reduction of the auto-correlation time of the topological charge in dynamical fermions simulations both at zero and finite temperature, allowing to avoid topology freezing down to lattice spacings as fine as a ∼ 0.02 fm. Therefore, this implementation of the Parallel Tempering on Boundary Conditions algorithm has the potential to substantially push forward the investigation of the QCD vacuum properties by means of lattice simulations.

Cohesive self-dual Yang-Mills modules over four manifolds

This research is motivated by Atiyah, Hitchin, and Singers paper Self-duality in Four-Dimensional Riemannian Geometry , which introduced a relationship between self-dual Yang-Mills fields on smooth manifolds and holomorphic vector bundles on their twistor spaces. Here, self-duality is a specific structure in 4-dimensional manifolds and Yang-Mills fields are gauge fields that satisfy Yang-Mills equations in 4-dimensions and are corresponded to the holomorphic bundles on twistor spaces. In this paper, we extend the relationship from vector bundles to a generalization of the Yang-Mills fields. To achieve this purpose, we apply Atiyah, Hitchin, and Singers theorem to cohesive modules, which was originally introduced by Block in in studying coherent sheaves over complex manifolds and the relations between homomorphic torus and its dual non-commutative torus. We introduce the notion of cohesive self-dual Yang-Mills modules and show that the twistor correspondence actually induces the equivalence between the dg category of cohesive self-dual Yang Mills modules P_(A_SD ) and the dg category of holomorphic cohesive modules P_(A_Hol ) on the twistor spaces.

Generating 4-dimensional wormholes with Yang–Mills Casimir sources

This work presents a new static and spherically symmetric traversable wormhole solution in General Relativity, which is supported by the quantum vacuum fluctuations associated with the Casimir effect of the Yang–Mills field confined between perfect chromometallic mirrors in (3+1) dimensions, recently fitted using first-principle numerical simulations. Initially, we employ a perturbative approach for x=mr≪1, where m represents the Casimir mass and r is the radial coordinate. This approach has proven to be a reasonable approximation when compared with the exact case in this regime. To find well-behaved redshift functions, we impose constraints on the free parameters. As expected, this solution recovers the electromagnetic-like Casimir solution for m=0. Analyzing the traversability conditions, we graphically find that all are satisfied for 0≤m≤0.17. On the other hand, all the energy conditions are violated, as usual in this context due to the quantum origin of the source. Stability from Tolman–Oppenheimer–Volkov (TOV) equation is guaranteed for all r and from the speed of sound for 0.16≤m≤0.18. Therefore, for 0.16≤m≤0.17, we will have a stable solution that satisfies all traversability conditions.

Confining strings in three-dimensional gauge theories beyond the Nambu-Gotō approximation

We carry out a systematic study of the effective bosonic string describing confining flux tubes in SU(N) Yang-Mills theories in three spacetime dimensions. While their low-energy properties are known to be universal and are described well by the Nambu-Gotō action, a non-trivial dependence on the gauge group is encoded in a series of undetermined subleading corrections in an expansion around the limit of an arbitrarily long string. We quantify the first two of these corrections by means of high-precision Monte Carlo simulations of Polyakov-loop correlators in the lattice regularization. We compare the results of novel lattice simulations for theories with N = 3 and 6 color charges, and report an improved estimate for the N = 2 case, discussing the approach to the large-N limit. Our results are compatible with analytical bounds derived from the S-matrix bootstrap approach. In addition, we also present a new test of the Svetitsky-Yaffe conjecture for the SU(3) theory in three dimensions, finding that the lattice results for the Polyakov-loop correlation function are in excellent agreement with the predictions of the Svetitsky-Yaffe mapping, which are worked out quantitatively applying conformal perturbation theory to the three-state Potts model in two dimensions. The implications of these results are discussed.

What can abelian gauge theories teach us about kinematic algebras?

The phenomenon of BCJ duality implies that gauge theories possess an abstract kinematic algebra, mirroring the non-abelian Lie algebra underlying the colour information. Although the nature of the kinematic algebra is known in certain cases, a full understanding is missing for arbitrary non-abelian gauge theories, such that one typically works outwards from well-known examples. In this paper, we pursue an orthogonal approach, and argue that simpler abelian gauge theories can be used as a testing ground for clarifying our understanding of kinematic algebras. We first describe how classes of abelian gauge fields are associated with well-defined subalgebras of the diffeomorphism algebra. By considering certain special subalgebras, we show that one may construct interacting theories, whose kinematic algebras are inherited from those already appearing in a related abelian theory. Known properties of (anti-)self-dual Yang-Mills theory arise in this way, but so do new generalisations, including self-dual electromagnetism coupled to scalar matter. Furthermore, a recently obtained non-abelian generalisation of the Navier-Stokes equation fits into a similar scheme, as does Chern-Simons theory. Our results provide useful input to further conceptual studies of kinematic algebras.

A Scaling Relation, Zm-Type Deconfinement Phases, and Imaginary Chemical Potentials in Finite Temperature Large-N Gauge Theories

Abstract We show that the effective potentials for the Polyakov loops in finite temperature SU$(N)$ gauge theories obey a certain scaling relation with respect to temperature in the large-N limit. This scaling relation strongly constrains the possible terms in the Polyakov loop effective potentials. Moreover, by using the effective potentials in the presence of imaginary chemical potentials or imaginary angular velocities in several models, we find that phase transitions to $Z_m$-type deconfinement phases ($Z_m$ phase) occur, where the eigenvalues of the Polyakov loop are distributed $Z_m$ symmetrically. Physical quantities in the $Z_m$ phase obey the scaling properties of the effective potential. The models include Yang–Mills (YM) theories, the bosonic BFSS matrix model, and ${\mathcal {N}}=4$ supersymmetric YM theory on $S^3$. Thus, the phase diagrams of large-N gauge theories with imaginary chemical potentials are very rich and the stable $Z_m$ phase would be ubiquitous. Monte-Carlo calculations also support this. As a related topic, we discuss the phase diagrams of large-N YM theories with real angular velocities in finite volume spaces.

Conservation laws of stress–energy tensor in Yang–Mills theory

In this paper we present a new identity to associate the conservation laws of stress–energy tensor with the field equations in Yang–Mills theory. The Lorentz force is included with a consistent formulation as in Maxwell theory.

The Casimir Effect in Finite-Temperature and Gravitational Scenarios

In this paper, we review some recent findings related to the Casimir effect. Initially, the thermal corrections to the vacuum Casimir energy density are calculated, for a quantum scalar field, whose modes propagate in the (3+1)-dimensional Euclidean spacetime, subject to a nontrivial compact boundary condition. Next, we analyze the Casimir effect induced by two parallel plates placed in a weak gravitational field background. Finally, we review the three-dimensional wormhole solutions sourced by the Casimir density and pressures associated with the quantum vacuum fluctuations of the Yang-Mills field.

A relationship between two-dimensional and four-dimensional space-time by comparing generalized two-dimensional Yang–Mills theory and Maxwell construction

Some important problems in science do not have analytical solutions in four dimensions including QCD, but they are integrable in two dimensions. For many years, scientists have been trying to find a relation between two-dimensional and four-dimensional space-time to explain the real problem in four dimensions by accurately solving the appropriate model in two dimensions. In this paper, an interesting relation between gYM2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$gY M_2$$\\end{document} (generalized two-dimensional Yang–Mills) and Maxwell construction has been found, which can be a starting point for finding more relations between two-dimensional and four-dimensional space-time, so this paper can play an important role in the advancement of science. For this purpose, first, the large-N behavior of the quartic-cubic generalized two-dimensional Yang–Mills U(N) on a sphere is investigated for finite cubic couplings. It is shown that there are two phase transitions one of which is of third order, which is similar to previous papers, and the other one is of second order, which is a novel result. Second, gYM2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$gY M_2$$\\end{document} (for G(z)=zm+λzn;m=4,6;n<m\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ G(z) = z^ m + \\lambda \\, z^n; m = 4, 6; n < m$$\\end{document}) and Maxwell construction are compared with each other and a relationship between two-dimensional space-time, which is integrable, and four-dimensional space-time is obtained.

Twisted circle compactification of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM and its holographic dual

We consider a compactification of 4D N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM, with SU(N) gauge group, on a circle with anti-periodic boundary conditions for the fermions. We couple the theory to a constant background gauge field along the circle for an abelian subgroup of the R-symmetry which allows to preserve four supersymmetries. The 3D effective theory exhibits gapped and ungapped phases, which we argue are holographically dual, respectively, to a supersymmetric soliton in AdS5 × S5, and a particular quotient of AdS5 × S5. The gapped phase corresponds to an IR 3D N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 supersymmetric Yang-Mills-Chern-Simons theory at level N, while the ungapped phase is naturally identified with the root of a Higgs branch in the 3D theory. We discuss the extension of the twisting procedure to maximally SUSY Yang-Mills theories in different dimensions, obtaining the relevant duals for 2D and 6D, and comment on the odd dimensional cases.

Domain walls in super Yang-Mills: worldvolume TQFTs and deconfinement from semiclassics on ℝ3× \U0001d54a1

This work studies domain walls between chirally-separated vacua in supersymmetric Yang-Mills theory (SYM) on ℝ3× \U0001d54a1 in the semiclassical limit. For all gauge groups we explicitly find the electric fluxes of all BPS domain walls and fully characterize the representation that they form under the global symmetry of SYM. We compute the characters of these representations formed by the semiclassical domain walls. We also compute these characters for the worldvolume TQFTs appearing in the literature for SU(N) and Sp(N) gauge groups. We find complete agreement between the two computations, providing thus a dynamical test of the proposed worldvolume TQFTs. We also propose a new worldvolume TQFT for E6 domain walls, subjecting it to the same tests. Finally, we study deconfinement of quarks on domain walls for all gauge groups. We show that for all gauge groups confining strings (stable in the abelianized regime) can end on domain walls, regardless of whether or not the group has a center.