10,402 research outputs found

    The holomorphic bosonic string

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    We present a holomorphic version of the bosonic string in the formalism of quantum field theory developed by Costello and collaborators. In this paper we focus on the case in which space-time is flat and construct a one-loop exact quantization. Starting from first principles, we arrive at the critical dimension as an obstruction to satisfying the quantum master equation. Moreover, we show how the factorization algebra recovers the BRST cohomology of the string and give another construction of the Gerstenhaber structure. Finally, we show how the factorization homology along closed manifolds encodes the determinant line bundle over the moduli space of Riemann surfaces.Comment: Fixed typos and clarified exposition. Modified Section

    A one-loop exact quantization of Chern-Simons theory

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    We examine Chern-Simons theory as a deformation of a 3-dimensional BF theory that is partially holomorphic and partially topological. In particular, we introduce a novel gauge that leads naturally to a one-loop exact quantization of this BF theory and Chern-Simons theory. This approach illuminates several important features of Chern-Simons theory, notably the bulk-boundary correspondence of Chern-Simons theory with chiral WZW theory. In addition to rigorously constructing the theory, we also explain how it applies to a large class of closely related 3-dimensional theories and some of the consequences for factorization algebras of observables.Comment: 35 pages, 1 figur

    Higher Kac-Moody algebras and symmetries of holomorphic field theories

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    We introduce a higher dimensional generalization of the affine Kac-Moody algebra using the language of factorization algebras. In particular, on any complex manifold there is a factorization algebra of "currents" associated to any Lie algebra. We classify local cocycles of these current algebras, and compare them to central extensions of higher affine algebras recently proposed by Faonte-Hennion-Kapranov. A central goal of this paper is to witness higher Kac-Moody algebras as symmetries of a class of holomorphic quantum field theories. In particular, we prove a generalization of the free field realization of an affine Kac-Moody algebra and also develop the theory of q-characters for this class of algebras in terms of factorization homology. Finally, we exhibit the "large N" behavior of higher Kac-Moody algebras and their relationship to symmetries of non-commutative field theories.Comment: All around improvements to exposition. Added Section 5: Large N Limit

    Factorization algebras and abelian CS/WZW-type correspondences

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    We develop a method of quantization for free field theories on manifolds with boundary where the bulk theory is topological in the direction normal to the boundary and a local boundary condition is imposed. Our approach is within the Batalin-Vilkovisky formalism. At the level of observables, the construction produces a stratified factorization algebra that in the bulk recovers the factorization algebra developed by Costello and Gwilliam. The factorization algebra on the boundary stratum enjoys a perturbative bulk-boundary correspondence with this bulk factorization algebra. A central example is the factorization algebra version of the abelian Chern-Simons/Wess-Zumino-Witten correspondence, but we examine higher dimensional generalizations that are related to holomorphic truncations of string theory and MM-theory and involve intermediate Jacobians.Comment: Small changes to version submitted for publicatio

    Chiral differential operators via via quantization of the holomorphic σ -model

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    ISBN 978-2-85629-919-7 This work would not have been possible without the support of several organizations. First, it was the open and stimulating atmosphere of the Max Planck Institute for Mathematics that made it so easy to begin our collaboration. Moreover, it is through the MPIM’s great generosity that we were able to continue work and finish the paper during several visits by VG and BW. Second, we benefited from the support and convivial setting of the Hausdorff Institute for Mathematics and its Trimester Program “Homotopy theory, manifolds, and field theories” during the summer of 2015. Third, the Oberwolfach Workshop “Factorization Algebras and Functorial Field Theories” in May 2016 allowed us all to gather in person and finish important discussions. In addition, OG enjoyed support from the National Science Foundation as a postdoctoral fellow under Award DMS-1204826, and BW enjoyed support as a graduate student research fellow under Award DGE-1324585. Finally, this research was carried out, in part, within the HSE University Basic Research Program and funded by the Russian Academic Excellence Project 5–100. For OG there is a large cast of mathematicians whose questions, conversation, and interest have kept these issues alive and provided myriad useful insights that are now hard to enumerate in detail. He thanks Kevin Costello for introducing him to the ÎČÎł system in graduate school—and for innumerable discussions since—as well as Dan Berwick-Evans, Ryan Grady, and Yuan Shen for grappling collaboratively with [15] throughout that period. Si Li’s many insights and questions have shaped this work substantially. Matt Szczesny’s guidance at the Northwestern CDO Workshop was crucial; his subsequent encouragement is much appreciated. OG would also like to thank Stephan Stolz and Peter Teichner for the still-running conversation about conformal field theory that influences strongly his approach to the subject. Finally, he thanks AndrĂ© Henriques, John Francis, and Scott Carnahan for letting him eavesdrop as they chatted about CDOs over a decade ago. BW feels fortunate to have stepped into this community early in his graduate work and has benefited from the support of many of the individuals mentioned above. First and foremost, he thanks his adviser Kevin Costello for guidance and Si Li for helping him to harness Feynman diagrams in the context of the BV formalism. He also thanks Ryan Grady, Matt Szczesny, and Stephan Stolz for invitations to talk about this project as well as valuable input on various aspects of it. In addition, numerous discussions with Dylan William Butson, Chris Elliott, and Philsang Yoo about perturbative QFT have informed his work. Finally, we would like to thank Matt Szczesny and James Ladouce for pointing out numerous typos and providing feedback on an earlier draft of this paper.Peer reviewedPostprin

    Objective assessment of stiffness in Achilles tendinopathy: a novel approach using the MyotonPRO

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    Objectives The aim of this study was to establish quantitative values for asymptomatic and symptomatic Achilles tendons. Design Cohort study with a single (cross-sectional) time point of patients diagnosed with unilateral Achilles tendinopathy and an asymptomatic group with comparative homogeneity. Methods A sample of 50 participants: 25 diagnosed with symptomatic unilateral Achilles tendinopathy (AT group) and 25 with asymptomatic Achilles tendons (control group 2). The asymptomatic side of the AT group was used as a control (control group 1). Measurements at 2 cm intervals on the tendon from its insertion at the calcaneum up to the musculotendinous junction were taken non-weight bearing (NWB) and weight bearing (WB) using the MyotonPRO. Results There was a significant (p<0.005) decrease in natural oscillation frequency (F) at points 2, 3 and 4 of the AT group (NWB condition) and points 2 and 3 for the WB condition. There was a significant (p<0.005) increase in logarithmic decrement (D) at points 2 and 3 signifying a decrease in elasticity. Dynamic stiffness (S) was significantly (p<0.005) reduced in the AT group at points 2 and 3 WB and point 3 WB. There was no significant difference in creep (C) observed between the symptomatic and asymptomatic tendons. There was a significant (p<0.005) increase in mechanical stress relaxation time (R) at point 2 NWB. There was a correlation between body weight and gender on tendon mechanics, with the symptomatic tendons. No significant differences were observed between the control group 1 and control group 2. Conclusions The MyotonPRO measured decreased stiffness over a section of the tendon corresponding clinically with Achilles tendinopathy. This may have potential in identifying risk of injury and informing rehabilitation, however further extensive research is required to generate baseline data for specific population groups monitoring variables over time. Age, gender and body mass index appear to have some bearing on the mechanical properties of the tendon but mainly in the tendinopathy group

    ATHLETIC IDENTITY AND HYPERCOMPETITIVENESS: IMPACT ON ATHLETES' ATTITUDES TOWARD PAIN AND SPORT-RELATED INJURY

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    The sporting world often praises and recognizes athletes who display a "fight-through-the-pain" mentality, putting the team and/or individual accolades before their own physical health or risk of further injury. However, some athletes' excessive drive to compete and win may potentially put them at higher risk for harm, both physically and psychologically, depending on their response to pain and injury. This study explored the impact of overly competitive attitudes on an athlete's ability to cope with pain and injury in sport. Specifically, responses on a pain coping attitudes inventory were examined in relation to measures of athletic identity and hypercompetitiveness for a sample of 114 intercollegiate athletes at a midwestern NCAA Division I school. Results were compared across gender and sport-orientation (team vs. individual) using 2-tailed analyses of variance and hierarchical multiple regression modeling. Findings from this study suggest that hypercompetitive attitudes are a stronger predictor than athletic identity of determining how an athlete will respond to injury. Results also indicate that individual- and team-oriented athletes display similar athletic identity, hypercompetitive attitudes, and pain coping ability. Furthermore, males in this sample demonstrated higher overall pain coping responses than females, regardless of sport orientation

    Isolation of Unknown Genes from Human Bone Marrow by Differental Screening and Single-Pass cDNA Sequences Determination

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    A cDNA sequencing project was initiated to characterize gene expression in human bone marrow and develop strategies to isolate novel genes. Forty-eight random cDNAs from total human bone marrow were subjected to single-pass DNA sequence analysis to determine a limited complexity of mRNAs expressed in the bone marrow. Overall, 8 cDNAs (17%) showed no similarity to known sequences. Information from DNA sequence analysis was used to develop a differential prescreen to subtract unwanted cDNAs and to enrich for unknown cDNAs. Forty-eight cDNAs that were negative with a complex probe were subject to single-pass DNA sequence determination. Of these prescreened cDNAs, the number of unknown sequences increased to 23 (48%). Unknown cDNAs were also characterized by RNA expression analysis using 25 different human leukemic cell lines. Of 13 unknown cDNAs tested, 10 were expressed in all cell types tested and 3 revealed a hematopoietic lineage-restricted expression pattern. Interestingly, while a total of only 96 bone marrow cDNAs were sequenced, 31 of these cDNAs represent sequences from unknown genes and 12 showed significant similarities to sequences in the data bases. One cDNA revealed a significant similarity to a serine/threonine-protein kinase at the amino acid level (56% identity for 123 amino acids) and may represent a previously unknown kinase. Differential screening techniques coupled with single-pass cDNA sequence analysis may prove to be a powerful and simple technique to examine developmental gene expression
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