Renormalization of vacuum expectation values in spontaneously broken gauge theories: Two-loop results

We complete the two-loop calculation of beta-functions for vacuum expectation values (VEVs) in gauge theories by the missing O(g^4)-terms. The full two-loop results are presented for generic and supersymmetric theories up to two-loop level in arbitrary R_xi-gauge. The results are obtained by means of a scalar background field, identical to our previous analysis. As a by-product, the two-loop scalar anomalous dimension for generic supersymmetric theories is presented. As an application we compute the beta-functions for VEVs and tan(beta) in the MSSM, NMSSM, and E6SSM.Comment: 13 pages, 1 figur

Graphs with Plane Outside-Obstacle Representations

An \emph{obstacle representation} of a graph consists of a set of polygonal obstacles and a distinct point for each vertex such that two points see each other if and only if the corresponding vertices are adjacent. Obstacle representations are a recent generalization of classical polygon--vertex visibility graphs, for which the characterization and recognition problems are long-standing open questions. In this paper, we study \emph{plane outside-obstacle representations}, where all obstacles lie in the unbounded face of the representation and no two visibility segments cross. We give a combinatorial characterization of the biconnected graphs that admit such a representation. Based on this characterization, we present a simple linear-time recognition algorithm for these graphs. As a side result, we show that the plane vertex--polygon visibility graphs are exactly the maximal outerplanar graphs and that every chordal outerplanar graph has an outside-obstacle representation.Comment: 12 pages, 7 figure

The Political Economy of Heterogeneous Development: Quartile Effects of Income and Education

Does development lead to the establishment of more democratic institutions? Over the past 50 years, the countries have illustratred two very distinct stages of political development—authoritarian states with low levels of freedom on one side and democracies with liberal institutions on the other. We develop a new empirical strategy that allows for the first time to estimate the effects of development as well as changing unobserved country effects in driving democracy at these different stages of political development. We find income and education have the least effect on democracy when authoritarian regimes are consolidated and only changing country effects can lead to political development. Ironically, it is in highly democratic and wealthy nations that income and education start to play a role; however greater wealth and better educated citizenry can both help and hurt democracy depending again on what the country’s institutional legacies are. Far from accepting the notion that much of the developing world is cursed by unchanging and poor long-run institutions, policy-makers should take note that with democratization we also see changing country-specific factors that in turn condition the difference income and education can make for democracy.democracy, economic development, quantile regression

Instantons on conical half-flat 6-manifolds

We present a general procedure to construct 6-dimensional manifolds with SU(3)-structure from SU(2)-structure 5-manifolds. We thereby obtain half-flat cylinders and sine-cones over 5-manifolds with Sasaki-Einstein SU(2)-structure. They are nearly Kahler in the special case of sine-cones over Sasaki-Einstein 5-manifolds. Both half-flat and nearly Kahler 6-manifolds are prominent in flux compactifications of string theory. Subsequently, we investigate instanton equations for connections on vector bundles over these half-flat manifolds. A suitable ansatz for gauge fields on these 6-manifolds reduces the instanton equation to a set of matrix equations. We finally present some of its solutions and discuss the instanton configurations obtained this way.Comment: 1+32 pages, 1 figure, v2: 6 references added, v2 accepted for publication in JHE

Two-loop results on the renormalization of vacuum expectation values and infrared divergences in the FDH scheme

Recent progress in the understanding of vacuum expectation values and of infrared divergences in different regularization schemes is reviewed. Vacuum expectation values are gauge and renormalization-scheme dependent quantities. Using a method based on Slavnov-Taylor identities, the renormalization properties could be better understood. The practical outcome is the computation of the beta functions for vacuum expectation values in general gauge theories. The infrared structure of gauge theory amplitudes depends on the regularization scheme. The well-known prediction of the infrared structure in CDR can be generalized to the FDH and DRED schemes and is in agreement with explicit computations of the quark and gluon form factors. We discuss particularly the correct renormalization procedure and the distinction between MSbar and DRbar renormalization. An important practical outcome are transition rules between CDR and FDH amplitudes.Comment: 8 pages, proceedings for Loops and Legs in Quantum Field Theory 2014, Weimar, German

Sasakian quiver gauge theories and instantons on cones over lens 5-spaces

We consider SU(3)-equivariant dimensional reduction of Yang-Mills theory over certain cyclic orbifolds of the 5-sphere which are Sasaki-Einstein manifolds. We obtain new quiver gauge theories extending those induced via reduction over the leaf spaces of the characteristic foliation of the Sasaki-Einstein structure, which are projective planes. We describe the Higgs branches of these quiver gauge theories as moduli spaces of spherically symmetric instantons which are SU(3)-equivariant solutions to the Hermitian Yang-Mills equations on the associated Calabi-Yau cones, and further compare them to moduli spaces of translationally-invariant instantons on the cones. We provide an explicit unified construction of these moduli spaces as K\"ahler quotients and show that they have the same cyclic orbifold singularities as the cones over the lens 5-spaces.Comment: v2: 54 pages, accepted for publication in Nuclear Physics

Coleridge and the rhetoric of power: the conflict between Coleridge’s poetic theory and practice

The purpose of this thesis is to investigate the poetry of S.T. Coleridge in relation to his idealist theories of the poetic imagination. According to his various writings on the function of the imagination, the act of poesis ought to reflect the internal principles of creation as manifested in nature. The primary imagination, as Coleridge defines it in Biographia Literaria, speaks the language of God; the secondary imagination (the medium for poetic creativity) strives to imitate this universal power within the language of men. Poetry is thus understood as the vehicle which activates the "whole soul", moving man towards a sympathetic appreciation of the world he inhabits. However, as I intend to demonstrate, Coleridge's poetic language proves consistently inadequate in providing a constubstantiality between the mind and nature. The arbitrary nature of words often undermine the poet's intentions, ironically providing an outlet for repressed desires and fears. This is reflected strongly in the nature of poetic diction which often achieves an artistic fluidity at the expense of theoretical conviction. By contrast, when Coleridge's poetry remains faithful to his views, the language is often forced and stilted. Modem critical theory, in its emphasis on the arbitrariness of the linguistic sign, can be useful in locating such a subversion of intended meaning within the romantic text. In my introduction, I shall discuss the generic term "romanticism " in relation to post-modernist literary theory m a manner which suggests that romantic discourse is already profoundly aware of inherit contradictions within its own creative process. Having established a correlation between romanticism and its twentieth century literary criticism, I shall investigate Coleridge's poetry in the terms of his own theory, which always suggests the duplicity of the literary imagination in its articulation of artistic distinctions (Imagination/Fancy; Imitation/Copy)

On Normal Modes of a Warped Throat

As shown in arXiv:hep-th/0405282, the warped deformed conifold has two bosonic massless modes, a pseudoscalar and a scalar, that are dual to the phase and the modulus of the baryonic condensates in the cascading gauge theory. We reconsider the scalar mode sector, mixing fluctuations of the NS-NS 2-form and the metric, and include non-zero 4-d momentum $k_\mu$. The resulting pair of coupled equations produce a discrete spectrum of $m_4^2=- k_\mu^2$ which is interpreted as the spectrum of $J^{PC}= 0^{+-}$ glueballs in the gauge theory. Similarly, we derive the spectrum of certain pseudoscalar glueballs with $J^{PC}= 0^{--}$, which originate from the decoupled fluctuations of the RR 2-form. We argue that each of the massive scalar or pseudoscalar modes we find belongs to a 4-d massive axial vector or vector supermultiplet. We also discuss our results in the context of a finite length throat embedded into a type IIB flux compactification.Comment: LaTeX, 29 pages, 4 eps figure

Stolen Plausibility

Access to justice advocates worry that heightened pleading standards best represented by Bell Atlantic Corp. v. Twombly and Ashcroft v. Iqbal are a difficult hurdle for plaintiffs. But they have entirely ignored a related development that may be an insurmountable one: the doctrine of stolen plausibility. Born at the same time the legal system has raised pleading standards, this doctrine holds that it is inherently illegitimate for plaintiffs to rely on litigation materials from third parties in their complaints, even where those materials furnish the only realistic source of information that would help plaintiffs satisfy heightened pleading standards and when the borrowed materials would make the complaint meritorious. To do this, courts have drawn on Federal Rules of Civil Procedure 11 and 12(f). This Article steps back from the narrow lens of these two Rules to examine the doctrine of stolen plausibility with broader considerations of fairness in mind. It makes a normative case for allowing plaintiffs to rely on third-party materials in their complaints to throw them a necessary lifeline in their struggles to survive motions to dismiss their complaints, to treat them the same as other parties in the legal system that rely on third parties\u27 work product, and to let them profit from government litigation materials designed to serve them above all else. It then demonstrates that neither the text nor the history of Rules 11 and 12(f) supports the doctrine of stolen plausibility. Finally, it asserts that the policy justifications that might support the doctrine of stolen plausibility-such as incentivizing plaintiffs to conduct diligent pre-suit investigations-are not strong enough to outweigh this Article\u27s fairness concerns