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Triviality from the exact renormalization group
Get PDFUsing the exact renormalization group, it is shown that no physically acceptable non-trivial fixed points, with positive anomalous dimension, exist for (i) O(N ) scalar field theory in four or more dimensions, (ii) non-compact, pure Abelian gauge theory in any dimension. It is then shown, for both theories in any dimension, that otherwise physically acceptable non-trivial fixed points with negative anomalous dimension are non-unitary. In addition, a very simple demonstration is given, directly from the exact renormalization group, that should a critical fixed point exist for either theory in any dimension, then the two-point correlation function exhibits the expected behaviour
Towards a non-abelian electric-magnetic symmetry: the skeleton group
Get PDFWe propose a unified electric-magnetic symmetry group in Yang-Mills theory, which we call the skeleton group. We work in the context of non-abelian unbroken gauge symmetry, and provide evidence for our proposal by relating the representation theory of the skeleton group to the labelling and fusion rules of charge sectors, and by showing how the skeleton group arises naturally in a gauge-fixed description of the theory. In particular we show that the labels of electric, magnetic and dyonic sectors in non-abelian Yang-Mills theory can be interpreted in terms of irreducible representations of the skeleton group. Decomposing tensor products of these representations thus gives candidate fusion rules for these charge sectors. We demonstrate consistency of these fusion rules with the known fusion rules of the purely electric or magnetic sectors, and extract new predictions for the fusion rules of dyonic sectors in particular cases. We also implement S-duality and show that the fusion rules obtained from the skeleton group commute with S-duality. As further evidence for the relevance of the skeleton group we consider a generalisation of ’t Hooft’s abelian gauge fixing procedure. We show that the skeleton group plays the role of an effective symmetry in this gauge, and argue that this gauge is particularly useful for exploring phases of the theory which generalise Alice electrodynamics
The classical capacity of quantum channels with memory
Get PDFWe investigate the classical capacity of two quantum channels with memory: a periodic channel with depolarizing channel branches, and a convex combination of depolarizing channels. We prove that the capacity is additive in both cases. As a result, the channel capacity is achieved without the use of entangled input states. In the case of a convex combination of depolarizing channels the proof provided can be extended to other quantum channels whose classical capacity has been proved to be additive in the memoryless case
Calculating a maximizer for Quantum mutual information
Get PDFWe obtain a maximizer for the quantum mutual information for classical information sent over the quantum amplitude damping channel. This is achieved by limiting the ensemble of input states to antipodal states, in the calculation of the product state capacity for the channel. We also consider the product state capacity of a convex combination of two memoryless channels and demonstrate in particular that it is in general not given by the minimum of the capacities of the respective memoryless channels
Geometry in Transition: A Model of Emergent Geometry
Get PDFWe study a three matrix model with global SO(3) symmetry containing at most quartic powers of the matrices. We find an exotic line of discontinuous transitions with a jump in the entropy, characteristic of a 1st order transition, yet with divergent critical fluctuations and a divergent specific heat with critical exponent α = 1/2. The low temperature phase is a geometrical one with gauge fields fluctuating on a round sphere. As the temperature increased the sphere evaporates in a transition to a pure matrix phase with no background geometrical structure. Both the geometry and gauge fields are determined dynamically. It is not difficult to invent higher dimensional models with essentially similar phenomenology. The model presents an appealing picture of a geometrical phase emerging as the system cools and suggests a scenario for the emergence of geometry in the early universe
GUTs in type IIB orientifold compactifications
Get PDFWe systematically analyse globally consistent SU(5) GUT models on inter-secting D7-branes in genuine Calabi-Yau orientifolds with O3-and O7-planes. Beyond the well-known tadpole and K-theory cancellation conditions there exist a number of additional subtle but quite restrictive constraints. For the realisation of SU(5) GUTs with gauge symmetry breaking via U(1)_Y flux we present two classes of suitable Calabi-Yau manifolds defined via del Pezzo transitions of the elliptically fibred hypersurface P_(1,1,1,6,9)[18] and of the Quin-tic P_(1,1,1,1,1)[5], respectively. To define an orientifold projection we classify all involutions on del Pezzo surfaces. We work out the model building prospects of these geometries and present five globally consistent string GUT models in detail, including a 3-generation SU(5) model with no exotics whatsoever. We also realise other phenomenological features such as the 10 10 5_H Yukawa cou-pling and comment on the possibility of moduli stabilisation, where we find an entire new set of so-called swiss-cheese type Calabi-Yau manifolds. It is expected that both the general constrained structure and the concrete models lift to F-theory vacua on compact Calabi-Yau fourfolds
A Theory of Topological Edges and Domain Walls
Get PDFWe investigate domain walls between topologically ordered phases in two spatial dimensions and present a simple but general framework from which their degrees of freedom can be understood. The approach we present exploits the results on topological symmetry breaking that we have introduced and presented elsewhere. After summarizing the method, we work out predictions for the spectrum of edge excitations and for the transport through edges in some representative examples. These include domain walls between the Abelian and non-Abelian topological phases of Kitaev’s honeycomb lattice model in a magnetic field, as well as recently proposed domain walls between spin polarized and unpolarized non-Abelian fractional quantum Hall states at different filling fractions
The instability of intersecting fuzzy spheres
Get PDFWe discuss the classical and quantum stability of general configurations rep-resenting many fuzzy spheres in dimensionally reduced Yang-Mills-Chern-Simons mod-els with and without supersymmetry. By performing one-loop perturbative calculations around such configurations, we find that intersecting fuzzy spheres are classically unsta-ble in the class of models studied in this paper. We also discuss the large-N limit of the one-loop effective action as a function of the distance of fuzzy spheres. This shows, in particular, that concentric fuzzy spheres with different radii, which are identified with the ’t Hooft-Polyakov monopoles, are perturbatively stable in the bosonic model and in the D = 10 supersymmetric model