Localization of N=4 Superconformal Field Theory on S^1 x S^3 and Index

We provide the geometrical meaning of the ${\cal N}=4$ superconformal index. With this interpretation, the ${\cal N}=4$ superconformal index can be realized as the partition function on a Scherk-Schwarz deformed background. We apply the localization method in TQFT to compute the deformed partition function since the deformed action can be written as a $\delta_\epsilon$-exact form. The critical points of the deformed action turn out to be the space of flat connections which are, in fact, zero modes of the gauge field. The one-loop evaluation over the space of flat connections reduces to the matrix integral by which the ${\cal N}=4$ superconformal index is expressed.Comment: 42+1 pages, 2 figures, JHEP style: v1.2.3 minor corrections, v4 major revision, conclusions essentially unchanged, v5 published versio

Super-A-polynomials for Twist Knots

We conjecture formulae of the colored superpolynomials for a class of twist knots $K_p$ where p denotes the number of full twists. The validity of the formulae is checked by applying differentials and taking special limits. Using the formulae, we compute both the classical and quantum super-A-polynomial for the twist knots with small values of p. The results support the categorified versions of the generalized volume conjecture and the quantum volume conjecture. Furthermore, we obtain the evidence that the Q-deformed A-polynomials can be identified with the augmentation polynomials of knot contact homology in the case of the twist knots.Comment: 22+16 pages, 16 tables and 5 figures; with a Maple program by Xinyu Sun and a Mathematica notebook in the ancillary files linked on the right; v2 change in appendix B, typos corrected and references added; v3 change in section 3.3; v4 corrections in Ooguri-Vafa polynomials and quantum super-A-polynomials for 7_2 and 8_1 are adde

Brane cosmological solutions in six-dimensional warped flux compactifications

We study cosmology on a conical brane in the six-dimensional Einstein-Maxwell-dilaton system, where the extra dimensions are compactified by a magnetic flux. We systematically construct exact cosmological solutions using the fact that the system is equivalently described by (6+n)-dimensional pure Einstein-Maxwell theory via dimensional reduction. In particular, we find a power-law inflationary solution for a general dilatonic coupling. When the dilatonic coupling is given by that of Nishino-Sezgin chiral supergravity, this reduces to the known solution which is not inflating. The power-law solution is shown to be the late-time attractor. We also investigate cosmological tensor perturbations in this model using the (6+n)-dimensional description. We obtain the separable equation of motion and find that there always exist a zero mode, while tachyonic modes are absent in the spectrum. The mass spectrum of Kaluza-Klein modes is obtained numerically.Comment: 12 pages, 2 figures; v2: references added; v3: version published in JCA

Constraints on chiral operators in N=2 SCFTs

Open Access, © The Authors. Article funded by SCOAP3. This article is distributed under the terms of the Creative Commons Attribution License ( CC-BY 4.0 ), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

Cartan subalgebras and the UCT problem, II

We show that outer approximately represenbtable actions of a finite cyclic group on UCT Kirchberg algebras satisfy a certain quasi-freeness type property if the corresponding crossed products satisfy the UCT and absorb a suitable UHF algebra tensorially. More concretely, we prove that for such an action there exists an inverse semigroup of homogeneous partial isometries that generates the ambient C*-algebra and whose idempotent semilattice generates a Cartan subalgebra. We prove a similar result for actions of finite cyclic groups with the Rokhlin property on UCT Kirchberg algebras absorbing a suitable UHF algebra. These results rely on a new construction of Cartan subalgebras in certain inductive limits of Cartan pairs. We also provide a characterisation of the UCT problem in terms of finite order automorphisms, Cartan subalgebras and inverse semigroups of partial isometries of the Cuntz algebra $\mathcal{O}_2$. This generalizes earlier work of the authors.Comment: minor revisions; final version, accepted for publication in Math. Ann.; 26 page

Generalized Toda Theory from Six Dimensions and the Conifold

Recently, a physical derivation of the Alday-Gaiotto-Tachikawa correspondence has been put forward. A crucial role is played by the complex Chern-Simons theory arising in the 3d-3d correspondence, whose boundary modes lead to Toda theory on a Riemann surface. We explore several features of this derivation and subsequently argue that it can be extended to a generalization of the AGT correspondence. The latter involves codimension two defects in six dimensions that wrap the Riemann surface. We use a purely geometrical description of these defects and find that the generalized AGT setup can be modeled in a pole region using generalized conifolds. Furthermore, we argue that the ordinary conifold clarifies several features of the derivation of the original AGT correspondence.Comment: 27+2 pages, 3 figure

Atrazine-Induced Aromatase Expression Is SF-1 Dependent: Implications for Endocrine Disruption in Wildlife and Reproductive Cancers in Humans

BACKGROUND: Atrazine is a potent endocrine disruptor that increases aromatase expression in some human cancer cell lines. The mechanism involves the inhibition of phosphodiesterase and subsequent elevation of cAMP. METHODS: We compared steroidogenic factor 1 (SF-1) expression in atrazine responsive and non-responsive cell lines and transfected SF-1 into nonresponsive cell lines to assess SF-1’s role in atrazine-induced aromatase. We used a luciferase reporter driven by the SF-1–dependent aromatase promoter (ArPII) to examine activation of this promoter by atrazine and the related simazine. We mutated the SF-1 binding site to confirm the role of SF-1. We also examined effects of 55 other chemicals. Finally, we examined the ability of atrazine and simazine to bind to SF-1 and enhance SF-1 binding to ArPII. RESULTS: Atrazine-responsive adrenal carcinoma cells (H295R) expressed 54 times more SF-1 than nonresponsive ovarian granulosa KGN cells. Exogenous SF-1 conveyed atrazine-responsiveness to otherwise nonresponsive KGN and NIH/3T3 cells. Atrazine induced binding of SF-1 to chromatin and mutation of the SF-1 binding site in ArPII eliminated SF-1 binding and atrazine-responsiveness in H295R cells. Out of 55 chemicals examined, only atrazine, simazine, and benzopyrene induced luciferase via ArPII. Atrazine bound directly to SF-1, showing that atrazine is a ligand for this “orphan” receptor. CONCLUSION: The current findings are consistent with atrazine’s endocrine-disrupting effects in fish, amphibians, and reptiles; the induction of mammary and prostate cancer in laboratory rodents; and correlations between atrazine and similar reproductive cancers in humans. This study highlights the importance of atrazine as a risk factor in endocrine disruption in wildlife and reproductive cancers in laboratory rodents and humans