Exact beta function from the holographic loop equation of large-N QCD_4

We construct and study a previously defined quantum holographic effective action whose critical equation implies the holographic loop equation of large-N QCD_4 for planar self-avoiding loops in a certain regularization scheme. We extract from the effective action the exact beta function in the given scheme. For the Wilsonean coupling constant the beta function is exacly one loop and the first coefficient agrees with its value in perturbation theory. For the canonical coupling constant the exact beta function has a NSVZ form and the first two coefficients agree with their value in perturbation theory.Comment: 42 pages, latex. The exponent of the Vandermonde determinant in the quantum effective action has been changed, because it has been employed a holomorphic rather than a hermitean resolution of identity in the functional integral. Beta function unchanged. New explanations and references added, typos correcte

Strings in flat space and pp waves from N=4{\cal N}=4 Super Yang Mills

We explain how the string spectrum in flat space and pp-waves arises from the large $N$ limit, at fixed $g^2_{YM}$, of U(N) ${\cal N} =4$ super Yang Mills. We reproduce the spectrum by summing a subset of the planar Feynman diagrams. We give a heuristic argument for why we can neglect other diagrams. We also discuss some other aspects of pp-waves and we present a matrix model associated to the DLCQ description of the maximally supersymmetric eleven dimensional pp-waves.Comment: 36 pages, 5 figures. v3: minor typos corrected, references adde

Universality of large N phase transitions in Wilson loop operators in two and three dimensions

The eigenvalue distribution of a Wilson loop operator of fixed shape undergoes a transition under scaling at infinite N. We derive a large N scaling function in a double scaling limit of the average characteristic polynomial associated with the Wilson loop operator in two dimensional QCD. We hypothesize that the transition in three and four dimensional large N QCD are also in the same universality class and provide a numerical test for our hypothesis in three dimensions.Comment: 43 pages, 1 table, 18 figures, uses JHEP3.cls, one reference added, replaced Figure 3 and a small change to eqn (4.8

Twisted local systems solve the (holographic) loop equation of large-N QCD_4

We construct a holographic map from the loop equation of large-N QCD in d=2 and d=4, for planar self-avoiding loops, to the critical equation of an equivalent effective action. The holographic map is based on two ingredients: an already proposed holographic form of the loop equation, such that the quantum contribution is reduced to a regularized residue; a new conformal map from the region encircled by the based loop to a cuspidal fundamental domain in the upper half-plane, such that the regularized residue vanishes at the cusp. As a check, we study the first coefficient of the beta function and that part of the second coefficient which arises from the rescaling anomaly, in passing from the Wilsonian to the canonically normalised (holographic) effective action.Comment: 42 pages, latex; abstract shortened and a reference added as suggested by the referee; typos in Eq.(72,76,77,82,83,84) correcte

Solving loop equations by Hitchin systems via holography in large-N QCD_4

For (planar) closed self-avoiding loops we construct a "holographic" map from the loop equations of large-N QCD_4 to an effective action defined over infinite rank Hitchin bundles. The effective action is constructed densely embedding Hitchin systems into the functional integral of a partially quenched or twisted Eguchi-Kawai model, by means of the resolution of identity into the gauge orbits of the microcanonical ensemble and by changing variables from the moduli fields of Hitchin systems to the moduli of the corresponding holomorphic de Rham local systems. The key point is that the contour integral that occurs in the loop equations for the de Rham local systems can be reduced to the computation of a residue in a certain regularization. The outcome is that, for self-avoiding loops, the original loop equations are implied by the critical equation of an effective action computed in terms of the localisation determinant and of the Jacobian of the change of variables to the de Rham local systems. We check, at lowest order in powers of the moduli fields, that the localisation determinant reproduces exactly the first coefficient of the beta function.Comment: 65 pages, late

Group measure space decomposition of II_1 factors and W*-superrigidity

We prove a "unique crossed product decomposition" result for group measure space II_1 factors arising from arbitrary free ergodic probability measure preserving (p.m.p.) actions of groups \Gamma in a fairly large family G, which contains all free products of a Kazhdan group and a non-trivial group, as well as certain amalgamated free products over an amenable subgroup. We deduce that if T_n denotes the group of upper triangular matrices in PSL(n,Z), then any free, mixing p.m.p. action of the amalgamated free product of PSL(n,Z) with itself over T_n, is W*-superrigid, i.e. any isomorphism between L^\infty(X) \rtimes \Gamma and an arbitrary group measure space factor L^\infty(Y) \rtimes \Lambda, comes from a conjugacy of the actions. We also prove that for many groups \Gamma in the family G, the Bernoulli actions of \Gamma are W*-superrigid.Comment: Final version. Some extra details have been added to improve the expositio

Human papilloma virus: Apprehending the link with carcinogenesis and unveiling new research avenues (Review)

Human papilloma viruses (HPV) are a small group of non-enveloped viruses belonging to the Papillomaviridae family with strong similarities to polyoma viruses. The viral particles consist of a genome in the form of a circular double-stranded DNA, encompassing eight open reading frames, as well as a non-enveloped icosahedral capsid. HPV infection is considered the most common sexually transmitted disease in both sexes and is strongly implicated in the pathogenesis of different types of cancer. 'High-risk' mucosal HPV types, predominantly types 16, 18, 31, 33 and 35, are associated with most cervical, penile, vulvar, vaginal, anal, oropharyngeal cancers and pre-cancers. Screening for HPV is necessary for the prognosis and for determining treatment strategies for cancer. Novel HPV markers, including proteomic and genomic markers, as well as anti-papillomavirus vaccines are currently available. The aim of this comprehensive review was to thoroughly present the updated information on virus development, cancer occurrence, treatment and prevention strategies, in an attempt to shed further light into the field, including novel research avenues

Neuroendocrine factors: The missing link in non-melanoma skin cancer (Review)

Non-melanoma skin cancer (NMSC) is the most common form of cancer worldwide, comprising 95% of all cutaneous malignancies and approximately 40% of all cancers. In spite of intensive efforts aimed towards awareness campaigns and sun-protective measures, epidemiological data indicate an increase in the incidence of NMSC. This category of skin cancers has many common environmental triggers. Arising primarily on sun-exposed skin, it has been shown that ultraviolet radiation is, in the majority of cases, the main trigger involved in the pathogenesis of NMSC. Aside from the well-known etiopathogenic factors, studies have indicated that several neuroactive factors are involved in the carcinogenesis of two of the most common types of NMSC, namely basal cell carcinoma (BCC) and squamous cell carcinoma (SCC), with the exception of penile SCC, for which a paucity of specific data on their pathogenic role exists. The complex interaction between the peripheral nervous system and target cells in the skin appears to be mediated by locally released neuroendocrine factors, such as catecholamines, substance P, calcitonin gene-related peptide and somatostatin, as well as neurohormones, such as proopiomelanocortin and its derived peptides, α-melanocyte-stimulating hormone and adrenocorticotropin. All these factors have been, at least at some point, a subject of debate regarding their precise role in the pathogenesis of NMSC. There is also a significant body of evidence indicating that psychological stress is a crucial impact factor influencing the course of skin cancers, including SCC and BCC. Numerous studies have suggested that neuroendocrine factor dysregulation, as observed in stress reactions, may be involved in tumorigenesis, accelerating the development and progression, and suppressing the regression of NMSC. Further studies are required in order to elucidate the exact mechanisms through which neuroactive molecules promote or inhibit cutaneous carcinogenesis, as this could lead to the development of more sophisticated and tailored treatment protocols, as well as open new perspectives in skin cancer research