Searching for continuous phase transitions in 5D SU(2) lattice gauge theory

We study the phase diagram of 5-dimensional SU(2) Yang-Mills theory on the lattice. We consider two extensions of the fundamental plaquette Wilson action in the search for the continuous phase transition suggested by the 4 + ϵ expansion. The extensions correspond to new terms in the action: i) a unit size plaquette in the adjoint representation or ii) a two-unit sided square plaquette in the fundamental representation. We use Monte Carlo to sample the first and second derivative of the entropy near the confinement phase transition, with lattices up to 125. While we exclude the presence of a second order phase transition in the parameter space we sampled for model i), our data is not conclusive in some regions of the parameter space of model ii).

DIAGRAMMATIC CONSTRUCTION OF REPRESENTATIONS OF SMALL QUANTUM $$ \mathfrak{sl} $$2

We provide a combinatorial description of the monoidal category generated by the fundamental representation of the small quantum group of $$ \mathfrak{sl} $$ sl 2 at a root of unity q of odd order. Our approach is diagrammatic, and it relies on an extension of the Temperley–Lieb category specialized at δ = −q − q−1.

The Fundamental Representation and Achievement Methods of a “Good Life” in Chinese Traditional Culture

A “good life” refers to a life phase in which people achieve a satisfying degree of spiritual value perception and emotional experience in the environment of “current” high material living standards, social harmony, fairness, and justice, and thus exclaim “good” from the heart. This article focuses on Chinese traditional culture's understanding of the “good life,” and attempted to summarize the “good life” in Chinese traditional fundamental characterization, as well as analyze the “good life” in Chinese traditional ways of implementation, using the literary method.

More on the flavor dependence of mϱ/fπ

In previous work, [arXiv:1905.01909], we have calculated the mϱ/fπ ratio in the chiral and continuum limit for SU(3) gauge theory coupled to Nf = 2, 3, 4, 5, 6 fermions in the fundamental representation. The main result was that this ratio displays no statistically significant Nf-dependence. In the present work we continue the study of the Nf-dependence by extending the simulations to Nf = 7, 8, 9, 10. Along the way we also study in detail the Nf-dependence of finite volume effects on low energy observables and a particular translational symmetry breaking unphysical, lattice artefact phase specific to staggered fermions.

Strong 1-boundedness of unimodular orthogonal free quantum groups

Recently, Brannan and Vergnioux showed that the orthogonal free quantum group factors [Formula: see text] have Jung’s strong [Formula: see text]-boundedness property, and hence are not isomorphic to free group factors. We prove an analogous result for the other unimodular case, where the parameter matrix is the standard symplectic matrix in [Formula: see text] dimensions [Formula: see text]. We compute free derivatives of the defining relations by introducing self-adjoint generators through a decomposition of the fundamental representation in terms of Pauli matrices, resulting in [Formula: see text]-boundedness of these generators. Moreover, we prove that under certain conditions, one can add elements to a [Formula: see text]-bounded set without losing [Formula: see text]-boundedness. In particular, this allows us to include the character of the fundamental representation, proving strong [Formula: see text]-boundedness.

Heroism, Resistance, and Sentiment: Two Events Full of Beethovenian Drama

Beethoven’s music has set the tone during different and diverse events in human history. It has been used in order to pinpoint major historical events, but it has been also used in order to represent ideas such as friendship of nations, freedom, and many others. There are two events though when the music of Beet­ ho ven has meant more than a fine and glorious tune for the Athenian public. These two events occurred under totally different circumstances, with the first being an incident involving a Fidelio performance during World War II in occupied Athens, and the second having to do with the death of the legendary conductor Dimitri Mitropoulos and his urn containing his ashes arriving in Athens. Although the two incidents are historically unconnected, they are very much underlined by the Beethovenian values rep­ resented within the actual score. In this study, I will present the historical framework of both events but also taking a step further will dare to connect these with values that have been attributed to Beethoven’s music in terms of fundamental representation.

Yang-Yang functions, monodromy and knot polynomials

We derive a structure of ℤ[t, t−1]-module bundle from a family of Yang-Yang functions. For the fundamental representation of the complex simple Lie algebra of classical type, we give explicit wall-crossing formula and prove that the monodromy representation of the ℤ[t, t−1]-module bundle is equivalent to the braid group representation induced by the universal R-matrices of Uh(g). We show that two transformations induced on the fiber by the symmetry breaking deformation and respectively the rotation of two complex parameters commute with each other.

Contributions of the Cartan generators in potentials between static sources

We investigate the contributions of the Cartan generators in the static potentials for various representations in the framework of the domain model of center vortices for SU(3) gauge theory. Using the center domains with the cores corresponding to only one Cartan generator [Formula: see text], already given as a particular proposal, leads to some concavities in the potentials for higher representations. Furthermore, the string tension of the fundamental representation is the same at Casimir scaling and [Formula: see text]-ality regimes. We add the contribution of the other Cartan generator [Formula: see text] to the potentials and therefore these shortcomings can be eliminated. However, we discuss that at intermediate range of distances the potentials induced by only [Formula: see text] agree with the Casimir scaling better than those corresponding to both Cartan generators.

Five-brane webs, Higgs branches and unitary/orthosymplectic magnetic quivers

We study the Higgs branch of 5d superconformal theories engineered from brane webs with orientifold five-planes. We propose a generalization of the rules to derive magnetic quivers from brane webs pioneered in [1], by analyzing theories that can be described with a brane web with and without O5 planes. Our proposed magnetic quivers include novel features, such as hypermultiplets transforming in the fundamental-fundamental representation of two gauge nodes, antisymmetric matter, and ℤ2 gauge nodes. We test our results by computing the Coulomb and Higgs branch Hilbert series of the magnetic quivers obtained from the two distinct constructions and find agreement in all cases.