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Features of gravity–Yang-Mills hierarchies in d-dimensions
Get PDFHigher dimensional, direct analogues of the usual d = 4 Einstein–Yang-Mills (EYM) systems are studied. These consist of the gravitational and Yang-Mills hierarchies in d = 4p dimensional spacetimes, both consisting of 2p-form curvature terms only. Regular and black hole solutions are constructed in 2p + 2 ≤ d ≤ 4p, in which dimensions the total mass-energy is finite, generalising the familiar Bartnik-McKinnon solutions in EYM theory for p = 1. In d = 4p, this similarity is complete. In the special case of d = 2p + 1, just beyond the finite energy range of d, exact solutions in closed form are found. Finally, d = 2p + 1 purely gravitational systems, whose solutions generalise the static d = 3 BTZ solutions, are discussed
The Quantum Hall Effect in Graphene: Emergent Modular Symmetry and the Semicircle Law
Get PDFLow-energy transport measurements in Quantum Hall systems have been argued to be governed by emergent modular symmetries whose predictions are robust against many of the detailed microscopic dynamics. We propose the recently-observed quantum Hall effect in graphene as a test of these ideas, and identify to this end a class of predictions for graphene which would follow from the same modular arguments. We are led to a suite of predictions for high mobility samples that differs from those obtained for the conventional quantum Hall effect in semiconductors, including: predictions for the locations of the quantum Hall plateaux; predictions for the positions of critical points on transitions between plateaux; a selection rule for which plateaux can be connected by low-temperature transitions; and a semi-circle law for conductivities traversed during these transitions. Many of these predictions appear to provide a good description of graphene measurements performed with intermediate-strength magnetic fields
No hair conjecture, non-Abelian hierarchies, and anti-de Sitter spacetime
Get PDFWe consider globally regular and black holes solutions for the Einstein-Yang-Mills system with negative cosmological constant in d−spacetime dimensions. We find that the ADM mass of the spherically symmetric solutions generically diverges for d > 4. Solutions with finite mass are found by considering corrections to the YM Lagrangean consisting in higher therm of the Yang–Mills hierarchy. Such systems can occur in the low energy effective action of string theory. A discussion of the main properties of the solutions and the differences with respect to the four dimensional case is presented. The mass of these configurations is computed by using a counterterm method
Counting BPS Operators in the Chiral Ring of N=2 Supersymmetric Gauge Theories or N=2 Braine Surgery
Get PDFThis note is presenting the generating functions which count the BPS operators in the chiral ring of a N = 2 quiver gauge theory that lives on N D3 branes probing an ALE singularity. The difficulty in this computation arises from the fact that this quiver gauge theory has a moduli space of vacua that splits into many branches – the Higgs, the Coulomb and mixed branches. As a result there can be operators which explore those different branches and the counting gets complicated by having to deal with such operators while avoiding over or under counting. The solution to this problem turns out to be very elegant and is presented in this note. Some surprises with “surgery” of generating functions arises
The medical school of Aghmacart, Queen's County
Get PDFThe following account, drawing on the researches of Fr Paul Walsh, Winifred Wulff, Nessa Ní Shéaghdha, Ronald Black and John Bannerman, summarises what is known of the school's origins and activities
Transfer matrix eigenvectors of the Baxter–Bazhanov–Stroganov τ_2-model for N = 2
Get PDFWe find a representation of the row-to-row transfer matrix of the Baxter-Bazhanov-Stroganov τ_2-model for N = 2 in terms of an integral over two commuting sets of Grassmann variables. Using this representation, we explicitly calculate transfer matrix eigenvectors and normalize them. It is also shown how form factors of the model can be expressed in terms of determinants and inverses of certain Toeplitz matrices
Drinfeld twist and general relativity with fuzzy spaces
Get PDFWe give a simplified formula for the star product on CP^n_L, which enables us to define a twist element suited for discussing a Drinfeld twist like structure on fuzzy complex projective spaces. The existence of such a twist will have several consequences for field theories on fuzzy spaces, some of which we discuss in the present paper. As expected, we find that the twist of the coproduct is trivial for the generators of isometries on CP^n_L. Furthermore, the twist allows us to define a covariant tensor calculus on CP^n_L from the perspective of the standard embedding of CP^n in at Euclidean space. That is, we find a representation of a truncated subgroup of the diffeomorphisms on CP^n on the algebra of functions on CP^n_L. Using this calculus, we eventually write down an Einstein-Hilbert action on the fuzzy sphere, which is invariant under twisted diffeomorphisms
A quantum version of the Feinstein Lemma and its application to channel coding
Get PDFIn this paper we develop a quantum version of Feinstein’s Lemma and use it to give a new proof of the direct channel coding theorem for transmission of classical information through a quantum memoryless channel. Moreover, we extend the lemma to a class of quantum channels with memory and thus obtain a bound for the achievable rates in the case of product state inputs
A Schematic Model of Generations of Quarks and Leptons
Get PDFWe propose a model of generations that has exactly three generations. This model has several attractive features: There is a simple mechanism to produce the CKM quark mixings and their neutrino analogs. There are definite predictions for particles of much higher mass than the quarks and leptons of the standard model, including the prediction of two-body decays without missing mass for the higher mass particles. There is a natural dark matter particle. A discussion of masses of the quarks suggests that the large mass differences between the generations could have a qualitative explanation, and there could be a simple way to make the u-d mass difference negative, but the c-s and t-b mass differences positive. The model also suggests a completely new scenario for the production, mass and decays of the Higgs meson that will be analysed in a separate paper