One Monopole with k Singularities

We present all charge one monopole solutions of the Bogomolny equation with k prescribed Dirac singularities for the gauge groups U(2), SO(3), or SU(2). We analyze these solutions comparing them to the previously known expressions for the cases of one or two singularities.Comment: 12 pages, LaTe

Angles in Fuzzy Disc and Angular Noncommutative Solitons

The fuzzy disc, introduced by the authors of Ref.[1], is a disc-shaped region in a noncommutative plane, and is a fuzzy approximation of a commutative disc. In this paper we show that one can introduce a concept of angles to the fuzzy disc, by using the phase operator and phase states known in quantum optics. We gave a description of a fuzzy disc in terms of operators and their commutation relations, and studied properties of angular projection operators. A similar construction for a fuzzy annulus is also given. As an application, we constructed fan-shaped soliton solutions of a scalar field theory on a fuzzy disc, which corresponds to a fan-shaped D-brane. We also applied this concept to the theory of noncommutative gravity that we proposed in Ref.[2]. In addition, possible connections to black hole microstates, holography and an experimental test of noncommutativity by laser physics are suggested.Comment: 24 pages, 12 figures; v2: minor mistake corrected in Eq.(3.21), and discussion adapted accordingly; v3: a further discussion on the algebra of the fuzzy disc added in subsection 3.2; v4: discussions improved and typos correcte

On the dynamical generation of the Maxwell term and scale invariance

Gauge theories with no Maxwell term are investigated in various setups. The dynamical generation of the Maxwell term is correlated to the scale invariance properties of the system. This is discussed mainly in the cases where the gauge coupling carries dimensions. The term is generated when the theory contains a scale explicitly, when it is asymptotically free and in particular also when the scale invariance is spontaneously broken. The terms are not generated when the scale invariance is maintained. Examples studied include the large $N$ limit of the $CP^{N-1}$ model in $(2+\epsilon)$ dimensions, a 3D gauged $\phi^6$ vector model and its supersymmetric extension. In the latter case the generation of the Maxwell term at a fixed point is explored. The phase structure of the $d=3$ case is investigated in the presence of a Chern-Simons term as well. In the supersymmetric $\phi^6$ model the emergence of the Maxwell term is accompanied by the dynamical generation of the Chern-Simons term and its multiplet and dynamical breaking of the parity symmetry. In some of the phases long range forces emerge which may result in logarithmic confinement. These include a dilaton exchange which plays a role also in the case when the theory has no gauge symmetry. Gauged Lagrangian realizations of the 2D coset models do not lead to emergent Maxwell terms. We discuss a case where the gauge symmetry is anomalous.Comment: 38 pages, 4 figures; v2 slightly improved, typos fixed, references added, published versio

Gauge fields and infinite chains of dualities

We show that the particle states of Maxwell's theory, in $D$ dimensions, can be represented in an infinite number of ways by using different gauge fields. Using this result we formulate the dynamics in terms of an infinite set of duality relations which are first order in space-time derivatives. We derive a similar result for the three form in eleven dimensions where such a possibility was first observed in the context of E11. We also give an action formulation for some of the gauge fields. In this paper we give a pedagogical account of the Lorentz and gauge covariant formulation of the irreducible representations of the Poincar\'e group, used previously in higher spin theories, as this plays a key role in our constructions. It is clear that our results can be generalised to any particle.Comment: 37 page

Spinning Conformal Correlators

We develop the embedding formalism for conformal field theories, aimed at doing computations with symmetric traceless operators of arbitrary spin. We use an index-free notation where tensors are encoded by polynomials in auxiliary polarization vectors. The efficiency of the formalism is demonstrated by computing the tensor structures allowed in n-point conformal correlation functions of tensors operators. Constraints due to tensor conservation also take a simple form in this formalism. Finally, we obtain a perfect match between the number of independent tensor structures of conformal correlators in d dimensions and the number of independent structures in scattering amplitudes of spinning particles in (d+1)-dimensional Minkowski space.Comment: 46 pages, 3 figures; V2: references added; V3: tiny misprint corrected in (A.9

Simplifying instanton corrections to N=4 SYM correlators

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Epistemic and Ontic Quantum Realities

Quantum theory has provoked intense discussions about its interpretation since its pioneer days. One of the few scientists who have been continuously engaged in this development from both physical and philosophical perspectives is Carl Friedrich von Weizsaecker. The questions he posed were and are inspiring for many, including the authors of this contribution. Weizsaecker developed Bohr's view of quantum theory as a theory of knowledge. We show that such an epistemic perspective can be consistently complemented by Einstein's ontically oriented position

Deep Inelastic Scattering in Conformal QCD

We consider the Regge limit of a CFT correlation function of two vector and two scalar operators, as appropriate to study small-x deep inelastic scattering in N=4 SYM or in QCD assuming approximate conformal symmetry. After clarifying the nature of the Regge limit for a CFT correlator, we use its conformal partial wave expansion to obtain an impact parameter representation encoding the exchange of a spin j Reggeon for any value of the coupling constant. The CFT impact parameter space is the three-dimensional hyperbolic space H3, which is the impact parameter space for high energy scattering in the dual AdS space. We determine the small-x structure functions associated to the exchange of a Reggeon. We discuss unitarization from the point of view of scattering in AdS and comment on the validity of the eikonal approximation. We then focus on the weak coupling limit of the theory where the amplitude is dominated by the exchange of the BFKL pomeron. Conformal invariance fixes the form of the vector impact factor and its decomposition in transverse spin 0 and spin 2 components. Our formalism reproduces exactly the general results predict by the Regge theory, both for a scalar target and for gamma*-gamma* scattering. We compute current impact factors for the specific examples of N=4 SYM and QCD, obtaining very simple results. In the case of the R-current of N=4 SYM, we show that the transverse spin 2 component vanishes. We conjecture that the impact factors of all chiral primary operators of N=4 SYM only have components with 0 transverse spin.Comment: 44+16 pages, 7 figures. Some correction

Impaired RNA incorporation and dimerization in live attenuated leader-variants of SIV(mac239)

BACKGROUND: The 5' untranslated region (UTR) or leader sequence of simian immunodeficiency virus (SIV(mac239)) is multifunctional and harbors the regulatory elements for viral replication, persistence, gene translation, expression, and the packaging and dimerization of viral genomic RNA (vRNA). We have constructed a series of deletions in the SIV(mac239 )leader sequence in order to determine the involvement of this region in both the packaging and dimerization of viral genomic RNA. We also assessed the impact of these deletions upon viral infectiousness, replication kinetics and gene expression in cell lines and monkey peripheral blood mononuclear cells (PBMC). RESULTS: Regions on both sides of the major splice donor (SD) were found to be necessary for the efficiency and specificity of viral genome packaging. However, stem-loop1 is critical for both RNA encapsidation and dimerization. Downstream elements between the splice donor and the initiation site of SIV-Gag have additive effects on RNA packaging and contribute to a lesser degree to RNA dimerization. The targeted disruption of structures on both sides of the SD also severely impacts viral infectiousness, gene expression and replication in both CEMx174 cells and rhesus PBMC. CONCLUSION: In the leader region of SIV(mac239), stem-loop1 functions as the primary determinant for both RNA encapsidation and dimerization. Downstream elements between the splice donor and the translational initiation site of SIV-Gag are classified as secondary determinants and play a role in dimerization. Collectively, these data signify a linkage between the primary encapsidation determinant of SIV(mac239 )and RNA dimerization

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects

We study the dynamics of four dimensional gauge theories with adjoint fermions for all gauge groups, both in perturbation theory and non-perturbatively, by using circle compactification with periodic boundary conditions for the fermions. There are new gauge phenomena. We show that, to all orders in perturbation theory, many gauge groups are Higgsed by the gauge holonomy around the circle to a product of both abelian and nonabelian gauge group factors. Non-perturbatively there are monopole-instantons with fermion zero modes and two types of monopole-anti-monopole molecules, called bions. One type are "magnetic bions" which carry net magnetic charge and induce a mass gap for gauge fluctuations. Another type are "neutral bions" which are magnetically neutral, and their understanding requires a generalization of multi-instanton techniques in quantum mechanics - which we refer to as the Bogomolny-Zinn-Justin (BZJ) prescription - to compactified field theory. The BZJ prescription applied to bion-anti-bion topological molecules predicts a singularity on the positive real axis of the Borel plane (i.e., a divergence from summing large orders in peturbation theory) which is of order N times closer to the origin than the leading 4-d BPST instanton-anti-instanton singularity, where N is the rank of the gauge group. The position of the bion--anti-bion singularity is thus qualitatively similar to that of the 4-d IR renormalon singularity, and we conjecture that they are continuously related as the compactification radius is changed. By making use of transseries and Ecalle's resurgence theory we argue that a non-perturbative continuum definition of a class of field theories which admit semi-classical expansions may be possible.Comment: 112 pages, 7 figures; v2: typos corrected, discussion of supersymmetric models added at the end of section 8.1, reference adde