Generalized quark-antiquark potential at weak and strong coupling

We study a two-parameter family of Wilson loop operators in N=4 supersymmetric Yang-Mills theory which interpolates smoothly between the 1/2 BPS line or circle and a pair of antiparallel lines. These observables capture a natural generalization of the quark-antiquark potential. We calculate these loops on the gauge theory side to second order in perturbation theory and in a semiclassical expansion in string theory to one-loop order. The resulting determinants are given in integral form and can be evaluated numerically for general values of the parameters or analytically in a systematic expansion around the 1/2 BPS configuration. We comment about the feasibility of deriving all-loop results for these Wilson loops.Comment: 43 pages: 15 comprising the main text and 25 for detailed appendice

On the perturbative S-matrix of generalized sine-Gordon models

Motivated by its relation to the Pohlmeyer reduction of AdS_5 x S^5 superstring theory we continue the investigation of the generalized sine-Gordon model defined by SO(N+1)/SO(N) gauged WZW theory with an integrable potential. Extending our previous work (arXiv:0912.2958) we compute the one-loop two-particle S-matrix for the elementary massive excitations. In the N = 2 case corresponding to the complex sine-Gordon theory it agrees with the charge-one sector of the quantum soliton S-matrix proposed in hep-th/9410140. In the case of N > 2 when the gauge group SO(N) is non-abelian we find a curious anomaly in the Yang-Baxter equation which we interpret as a gauge artifact related to the fact that the scattered particles are not singlets under the residual global subgroup of the gauge group

From correlation functions to scattering amplitudes

We study the correlators of half-BPS protected operators in N=4 super-Yang-Mills theory, in the limit where the positions of the adjacent operators become light-like separated. We compute the loop corrections by means of Lagrangian insertions. The divergences resulting from the light-cone limit are regularized by changing the dimension of the integration measure over the insertion points. Switching from coordinates to dual momenta, we show that the logarithm of the correlator is identical with twice the logarithm of the matching MHV gluon scattering amplitude. We present a number of examples of this new relation, at one and two loops.Comment: typos corrected, references adde

Topological Lattice Actions

We consider lattice field theories with topological actions, which are invariant against small deformations of the fields. Some of these actions have infinite barriers separating different topological sectors. Topological actions do not have the correct classical continuum limit and they cannot be treated using perturbation theory, but they still yield the correct quantum continuum limit. To show this, we present analytic studies of the 1-d O(2) and O(3) model, as well as Monte Carlo simulations of the 2-d O(3) model using topological lattice actions. Some topological actions obey and others violate a lattice Schwarz inequality between the action and the topological charge Q. Irrespective of this, in the 2-d O(3) model the topological susceptibility \chi_t = \l/V is logarithmically divergent in the continuum limit. Still, at non-zero distance the correlator of the topological charge density has a finite continuum limit which is consistent with analytic predictions. Our study shows explicitly that some classically important features of an action are irrelevant for reaching the correct quantum continuum limit.Comment: 38 pages, 12 figure

Loop Quantum Gravity a la Aharonov-Bohm

The state space of Loop Quantum Gravity admits a decomposition into orthogonal subspaces associated to diffeomorphism equivalence classes of spin-network graphs. In this paper I investigate the possibility of obtaining this state space from the quantization of a topological field theory with many degrees of freedom. The starting point is a 3-manifold with a network of defect-lines. A locally-flat connection on this manifold can have non-trivial holonomy around non-contractible loops. This is in fact the mathematical origin of the Aharonov-Bohm effect. I quantize this theory using standard field theoretical methods. The functional integral defining the scalar product is shown to reduce to a finite dimensional integral over moduli space. A non-trivial measure given by the Faddeev-Popov determinant is derived. I argue that the scalar product obtained coincides with the one used in Loop Quantum Gravity. I provide an explicit derivation in the case of a single defect-line, corresponding to a single loop in Loop Quantum Gravity. Moreover, I discuss the relation with spin-networks as used in the context of spin foam models.Comment: 19 pages, 1 figure; v2: corrected typos, section 4 expanded

Seiberg-Witten and "Polyakov-like" magnetic bion confinements are continuously connected

We study four-dimensional N=2 supersymmetric pure-gauge (Seiberg-Witten) theory and its N=1 mass perturbation by using compactification S**1 x R**3. It is well known that on R**4 (or at large S**1) the perturbed theory realizes confinement through monopole or dyon condensation. At small S**1, we demonstrate that confinement is induced by a generalization of Polyakov's three-dimensional instanton mechanism to a locally four-dimensional theory - the magnetic bion mechanism - which also applies to a large class of nonsupersymmetric theories. Using a large- vs. small-L Poisson duality, we show that the two mechanisms of confinement, previously thought to be distinct, are in fact continuously connected.Comment: 49 pages, 5 figure

Global Retinoblastoma Treatment Outcomes Association with National Income Level

Purpose: To compare metastasis-related mortality, local treatment failure, and globe salvage after retinoblastoma in countries with different national income levels. Design: International, multicenter, registry-based retrospective case series. Participants: Two thousand one hundred ninety patients, 18 ophthalmic oncology centers, and 13 countries on 6 continents. Methods: Multicenter registry-based data were pooled from retinoblastoma patients enrolled between January 2001 and December 2013. Adequate data to allow American Joint Committee on Cancer staging, eighth edition, and analysis for the level, as defined by the 2017 United Nations World Population Prospects, and included high-income countries (HICs), upper middle-income countries (UMICs), and lower middle-income countries (LMICs). Patient survival was estimated with the Kaplan-Meier method. Logistic and Cox proportional hazards regression models were used to determine associations between national income and treatment outcomes. Main Outcome Measures: Metastasis-related mortality and local treatment failure (defined as use of secondary enucleation or external beam radiation therapy). Results: Most (60%) study patients resided in UMICs and LMICs. The global median age at diagnosis was 17.0 months and higher in UMICs (20.0 months) and LMICs (20.0 months) than HICs (14.0 months; P < 0.001). Patients in UMICs and LMICs reported higher rates of disease-specific metastasis-related mortality and local treatment failure. As compared with HICs, metastasis-related mortality was 10.3-fold higher for UMICs and 9.3-fold higher for LMICs, and the risk for local treatment failure was 2.2-fold and 1.6-fold higher, respectively (all P < 0.001). Conclusions: This international, multicenter, registry-based analysis of retinoblastoma management revealed that lower national income levels were associated with significantly higher rates of metastasis-related mortality, local treatment failure, and lower globe salvage. (C) 2020 by the American Academy of Ophthalmology.Peer reviewe

Spin chemistry investigation of peculiarities of photoinduced electron transfer in donor-acceptor linked system

Photoinduced intramolecular electron transfer in linked systems, (R,S)- and (S,S)-naproxen-N-methylpyrrolidine dyads, has been studied by means of spin chemistry methods [magnetic field effect and chemically induced dynamic nuclear polarization (CIDNP)]. The relative yield of the triplet state of the dyads in different magnetic field has been measured, and dependences of the high-field CIDNP of the N-methylpyrrolidine fragment on solvent polarity have been investigated. However, both (S,S)- and (R,S)-enantiomers demonstrate almost identical CIDNP effects for the entire range of polarity. It has been demonstrated that the main peculiarities of photoprocesses in this linked system are connected with the participation of singlet exciplex alongside with photoinduced intramolecular electron transfer in chromophore excited state quenching.This work was supported by the grants 08-03-00372 and 11-03-01104 of the Russian Foundation for Basic Research, and the grant of Priority Programs of the Russian Academy of Sciences, nr. 5.1.5.Magin, I.; Polyakov, N.; Khramtsova, E.; Kruppa, A.; Stepanov, A.; Purtov, P.; Leshina, T.... (2011). Spin chemistry investigation of peculiarities of photoinduced electron transfer in donor-acceptor linked system. Applied Magnetic Resonance. 41(2-4):205-220. https://doi.org/10.1007/s00723-011-0288-3S205220412-4J.S. Park, E. Karnas, K. Ohkubo, P. Chen, K.M. Kadish, S. Fukuzumi, C.W. Bielawski, T.W. Hudnall, V.M. Lynch, J.L. Sessler, Science 329, 1324–1327 (2010)S.Y. Reece, D.G. Nocera, Annu. Rev. Biochem. 78, 673–699 (2009)M.S. Afanasyeva, M.B. Taraban, P.A. Purtov, T.V. Leshina, C.B. Grissom, J. Am. Chem. Soc. 128, 8651–8658 (2006)M.A. Fox, M. Chanon, in Photoinduced Electron Transfer. C: Photoinduced Electron Transfer Reactions: Organic Substrates (Elsevier, New York, 1988), p. 754P.J. Hayball, R.L. Nation, F. Bochner, Chirality 4, 484–487 (1992)N. Suesa, M.F. Fernandez, M. Gutierrez, M.J. Rufat, E. Rotllan, L. Calvo, D. Mauleon, G. Carganico, Chirality 5, 589–595 (1993)A.M. Evans, J. Clin. Pharmacol. 36, 7–15 (1996)Y. Inoue, T. Wada, S. Asaoka, H. Sato, J.-P. Pete, Chem Commun. 4, 251–259 (2000)T. Yorozu, K. Hayashi, M. Irie, J. Am. Chem. Soc. 103, 5480–5548 (1981)N.J. Turro, in Modern Molecular Photochemistry (Benjamin/Cummings, San Francisco, 1978)K.M. Salikhov, Y.N. Molin, R.Z. Sagdeev, A.L. Buchachenko, in Spin Polarization and Magnetic Field Effects in Radical Reactions (Akademiai Kiado, Budapest, 1984), p. 419E.A. Weiss, M.A. Ratner, M.R. Wasielewski, J. Phys. Chem. A 107, 3639–3647 (2003)A.S. Lukas, P.J. Bushard, E.A. Weiss, M.R. Wasielewski, J. Am. Chem. Soc. 125, 3921–3930 (2003)R. Nakagaki, K. Mutai, M. Hiramatsu, H. Tukada, S. Nakakura, Can. J. Chem. 66, 1989–1996 (1988)M.C. Jim′enez, U. Pischel, M.A. Miranda, J. Photochem. Photobiol. C Photochem. Rev. 8, 128–142 (2007)S. Abad, U. Pischel, M.A. Miranda, Photochem. Photobiol. Sci. 4, 69–74 (2005)U. Pischel, S. Abad, L.R. Domingo, F. Bosca, M.A. Miranda, Angew. Chem. Int. Ed. 42, 2531–2534 (2003)G.L. Closs, R.J. Miller, J. Am. Chem. Soc. 101, 1639–1641 (1979)G.L. Closs, R.J. Miller, J. Am. Chem. Soc. 103, 3586–3588 (1981)M. Goez, Chem. Phys. Lett. 188, 451–456 (1992)I.F. Molokov, Y.P. Tsentalovich, A.V. Yurkovskaya, R.Z. Sagdeev, J. Photochem. Photobiol. A 110, 159–165 (1997)U. Pischel, S. Abad, M.A. Miranda, Chem. Commun. 9, 1088–1089 (2003)H. Hayashi, S. Nagakura, Bull. Chem. Soc. Jpn. 57, 322–328 (1984)Y. Sakaguchi, H. Hayashi, S. Nagakura, Bull. Chem. Soc. Jpn. 53, 39–42 (1980)H. Yonemura, H. Nakamura, T. Matsuo, Chem. Phys. Lett. 155, 157–161 (1989)N. Hata, M. Hokawa, Chem. Lett. 10, 507–510 (1981)M. Shiotani, L. Sjoeqvist, A. Lund, S. Lunell, L. Eriksson, M.B. Huang, J. Phys. Chem. 94, 8081–8090 (1990)E. Schaffner, H. Fischer, J. Phys. Chem. 100, 1657–1665 (1996)Y. Mori, Y. Sakaguchi, H. Hayashi, Chem. Phys. Lett. 286, 446–451 (1998)I.M. Magin, A.I. Kruppa, P.A. Purtov, Chem. Phys. 365, 80–84 (2009)K.K. Barnes, Electrochemical Reactions in Nonaqueous Systems (M. Dekker, New York, 1970), p. 560J. Bargon, J. Am. Chem. Soc. 99, 8350–8351 (1977)M. Goez, I. Frisch, J. Phys. Chem. A 106, 8079–8084 (2002)A.K. Chibisov, Russ. Chem. Rev. 50, 615–629 (1981)J. Goodman, K. Peters, J. Am. Chem. Soc. 107, 1441–1442 (1985)H. Cao, Y. Fujiwara, T. Haino, Y. Fukazawa, C.-H. Tung, Y. Tanimoto, Bull. Chem. Soc. Jpn. 69, 2801–2813 (1996)P.A. Purtov, A.B. Doktorov, Chem. Phys. 178, 47–65 (1993)A.I. Kruppa, O.I. Mikhailovskaya, T.V. Leshina, Chem. Phys. Lett. 147, 65–71 (1988)M.E. Michel-Beyerle, R. Haberkorn, W. Bube, E. Steffens, H. Schröder, H.J. Neusser, E.W. Schlag, H. Seidlitz, Chem. Phys. 17, 139–145 (1976)K. Schulten, H. Staerk, A. Weller, H.-J. Werner, B. Nickel, Z. Phys. Chem. 101, 371–390 (1976)K. Gnadig, K.B. Eisenthal, Chem. Phys. Lett. 46, 339–342 (1977)T. Nishimura, N. Nakashima, N. Mataga, Chem. Phys. Lett. 46, 334–338 (1977)M.G. Kuzmin, I.V. Soboleva, E.V. Dolotova, D.N. Dogadkin, High Eng. Chem. 39, 86–96 (2005

Movement Timing and Invariance Arise from Several Geometries

Human movements show several prominent features; movement duration is nearly independent of movement size (the isochrony principle), instantaneous speed depends on movement curvature (captured by the 2/3 power law), and complex movements are composed of simpler elements (movement compositionality). No existing theory can successfully account for all of these features, and the nature of the underlying motion primitives is still unknown. Also unknown is how the brain selects movement duration. Here we present a new theory of movement timing based on geometrical invariance. We propose that movement duration and compositionality arise from cooperation among Euclidian, equi-affine and full affine geometries. Each geometry posses a canonical measure of distance along curves, an invariant arc-length parameter. We suggest that for continuous movements, the actual movement duration reflects a particular tensorial mixture of these canonical parameters. Near geometrical singularities, specific combinations are selected to compensate for time expansion or compression in individual parameters. The theory was mathematically formulated using Cartan's moving frame method. Its predictions were tested on three data sets: drawings of elliptical curves, locomotion and drawing trajectories of complex figural forms (cloverleaves, lemniscates and limaçons, with varying ratios between the sizes of the large versus the small loops). Our theory accounted well for the kinematic and temporal features of these movements, in most cases better than the constrained Minimum Jerk model, even when taking into account the number of estimated free parameters. During both drawing and locomotion equi-affine geometry was the most dominant geometry, with affine geometry second most important during drawing; Euclidian geometry was second most important during locomotion. We further discuss the implications of this theory: the origin of the dominance of equi-affine geometry, the possibility that the brain uses different mixtures of these geometries to encode movement duration and speed, and the ontogeny of such representations

Mitochondrial Morphogenesis, Dendrite Development, and Synapse Formation in Cerebellum Require both Bcl-w and the Glutamate Receptor δ2

Bcl-w belongs to the prosurvival group of the Bcl-2 family, while the glutamate receptor δ2 (Grid2) is an excitatory receptor that is specifically expressed in Purkinje cells, and required for Purkinje cell synapse formation. A recently published result as well as our own findings have shown that Bcl-w can physically interact with an autophagy protein, Beclin1, which in turn has been shown previously to form a protein complex with the intracellular domain of Grid2 and an adaptor protein, nPIST. This suggests that Bcl-w and Grid2 might interact genetically to regulate mitochondria, autophagy, and neuronal function. In this study, we investigated this genetic interaction of Bcl-w and Grid2 through analysis of single and double mutant mice of these two proteins using a combination of histological and behavior tests. It was found that Bcl-w does not control the cell number in mouse brain, but promotes what is likely to be the mitochondrial fission in Purkinje cell dendrites, and is required for synapse formation and motor learning in cerebellum, and that Grid2 has similar phenotypes. Mice carrying the double mutations of these two genes had synergistic effects including extremely long mitochondria in Purkinje cell dendrites, and strongly aberrant Purkinje cell dendrites, spines, and synapses, and severely ataxic behavior. Bcl-w and Grid2 mutations were not found to influence the basal autophagy that is required for Purkinje cell survival, thus resulting in these phenotypes. Our results demonstrate that Bcl-w and Grid2 are two critical proteins acting in distinct pathways to regulate mitochondrial morphogenesis and control Purkinje cell dendrite development and synapse formation. We propose that the mitochondrial fission occurring during neuronal growth might be critically important for dendrite development and synapse formation, and that it can be regulated coordinately by multiple pathways including Bcl-2 and glutamate receptor family members