A realisation of Lorentz algebra in Lorentz violating theory

A Lorentz non-invariant higher derivative effective action in flat spacetime, characterised by a constant vector, can be made invariant under infinitesimal Lorentz transformations by restricting the allowed field configurations. These restricted fields are defined as functions of the background vector in such a way that background dependance of the dynamics of the physical system is no longer manifest. We show here that they also provide a field basis for the realisation of Lorentz algebra and allow the construction of a Poincar\'e invariant symplectic two form on the covariant phase space of the theory.Comment: text body edited, reference adde

Hypercommutative operad as a homotopy quotient of BV

We give an explicit formula for a quasi-isomorphism between the operads Hycomm (the homology of the moduli space of stable genus 0 curves) and BV/$\Delta$ (the homotopy quotient of Batalin-Vilkovisky operad by the BV-operator). In other words we derive an equivalence of Hycomm-algebras and BV-algebras enhanced with a homotopy that trivializes the BV-operator. These formulas are given in terms of the Givental graphs, and are proved in two different ways. One proof uses the Givental group action, and the other proof goes through a chain of explicit formulas on resolutions of Hycomm and BV. The second approach gives, in particular, a homological explanation of the Givental group action on Hycomm-algebras.Comment: minor corrections added, to appear in Comm.Math.Phy

Geometric Hamiltonian Formalism for Reparametrization Invariant Theories with Higher Derivatives

Reparametrization invariant Lagrangian theories with higher derivatives are considered. We investigate the geometric structures behind these theories and construct the Hamiltonian formalism in a geometric way. The Legendre transformation which corresponds to the transition from the Lagrangian formalism to the Hamiltonian formalism is non-trivial in this case. The resulting phase bundle, i.e. the image of the Legendre transformation, is a submanifold of some cotangent bundle. We show that in our construction it is always odd-dimensional. Therefore the canonical symplectic two-form from the ambient cotangent bundle generates on the phase bundle a field of the null-directions of its restriction. It is shown that the integral lines of this field project directly to the extremals of the action on the configuration manifold. Therefore this naturally arising field is what is called the Hamilton field. We also express the corresponding Hamilton equations through the generilized Nambu bracket.Comment: 19 page

Development of Learning Objectives to Guide Enhancement of Chronic Disease Prevention and Management Curricula in Undergraduate Medical Education

Phenomenon: Chronic disease is a leading cause of death and disability in the United States. With an increase in the demand for healthcare and rising costs related to chronic care, physicians need to be better trained to address chronic disease at various stages of illness in a collaborative and cost-effective manner. Specific and measurable learning objectives are key to the design and evaluation of effective training, but there has been no consensus on chronic disease learning objectives appropriate to medical student education. Approach: Wagner’sChronic Care Model (CCM) was selected as a theoretical framework to guide development of an enhanced chronic dis-ease prevention and management (CDPM) curriculum. Findings of a literature review of CDPM competencies, objectives, and topical statements were mapped to each of the six domains of the CCM to understand the breadth of existing learning topics within each domain. At an in-person meeting, medical educators prepared a survey for the modified Delphi approach. Attendees iden-tified 51 possible learning objectives from the literature review mapping, rephrased the CCM domains as competencies, constructed possible CDPM learning objectives for each competency with the goal of reaching multi-institutional consensus on a limited number of CDPM learning objectives that would be feasible for institutions to use to guide enhancement of medical student curricula related to CDPM. After the meeting, the group developed a survey which included 39 learning objectives. In the study phase of the modified Delphi approach, 32 physician CDPM experts and educators completed an online survey to prioritize the top 20 objectives. The next step occurred at a CDPM interest group in-person meeting with the goal of identifying the top 10 objectives. Findings: The CCM domains were reframed as the following competencies for medical student education: patient self-care management, decision support, clinical information systems, community resources, delivery systems and teams, and health system practice and improvement. Eleven CDPM learning objectives were identified within the six competencies that were most important in developing curriculum for medical students. Insights: These learning objectives cut across education on the prevention and management of individual chronic diseases and frame chronic disease care as requiring the health system science competencies identified in the CCM. They are intended to be used in combination with traditional disease-specific pathophysiology and treatment objectives. Additional efforts are needed to identify specific curricular strategies and assessment tools for each learning objective

Extending the Belavin-Knizhnik "wonderful formula" by the characterization of the Jacobian

A long-standing question in string theory is to find the explicit expression of the bosonic measure, a crucial issue also in determining the superstring measure. Such a measure was known up to genus three. Belavin and Knizhnik conjectured an expression for genus four which has been proved in the framework of the recently introduced vector-valued Teichmueller modular forms. It turns out that for g>3 the bosonic measure is expressed in terms of such forms. In particular, the genus four Belavin-Knizhnik "wonderful formula" has a remarkable extension to arbitrary genus whose structure is deeply related to the characterization of the Jacobian locus. Furthermore, it turns out that the bosonic string measure has an elegant geometrical interpretation as generating the quadrics in P^{g-1} characterizing the Riemann surface. All this leads to identify forms on the Siegel upper half-space that, if certain conditions related to the characterization of the Jacobian are satisfied, express the bosonic measure as a multiresidue in the Siegel upper half-space. We also suggest that it may exist a super analog on the super Siegel half-space.Comment: 15 pages. Typos corrected, refs. and comments adde

Challenges of beta-deformation

A brief review of problems, arising in the study of the beta-deformation, also known as "refinement", which appears as a central difficult element in a number of related modern subjects: beta \neq 1 is responsible for deviation from free fermions in 2d conformal theories, from symmetric omega-backgrounds with epsilon_2 = - epsilon_1 in instanton sums in 4d SYM theories, from eigenvalue matrix models to beta-ensembles, from HOMFLY to super-polynomials in Chern-Simons theory, from quantum groups to elliptic and hyperbolic algebras etc. The main attention is paid to the context of AGT relation and its possible generalizations.Comment: 20 page

Superpolynomials for toric knots from evolution induced by cut-and-join operators

The colored HOMFLY polynomials, which describe Wilson loop averages in Chern-Simons theory, possess an especially simple representation for torus knots, which begins from quantum R-matrix and ends up with a trivially-looking split W representation familiar from character calculus applications to matrix models and Hurwitz theory. Substitution of MacDonald polynomials for characters in these formulas provides a very simple description of "superpolynomials", much simpler than the recently studied alternative which deforms relation to the WZNW theory and explicitly involves the Littlewood-Richardson coefficients. A lot of explicit expressions are presented for different representations (Young diagrams), many of them new. In particular, we provide the superpolynomial P_[1]^[m,km\pm 1] for arbitrary m and k. The procedure is not restricted to the fundamental (all antisymmetric) representations and the torus knots, still in these cases some subtleties persist.Comment: 23 pages + Tables (51 pages

3d-3d Correspondence Revisited

In fivebrane compactifications on 3-manifolds, we point out the importance of all flat connections in the proper definition of the effective 3d N=2 theory. The Lagrangians of some theories with the desired properties can be constructed with the help of homological knot invariants that categorify colored Jones polynomials. Higgsing the full 3d theories constructed this way recovers theories found previously by Dimofte-Gaiotto-Gukov. We also consider the cutting and gluing of 3-manifolds along smooth boundaries and the role played by all flat connections in this operation.Comment: 43 pages + 1 appendix, 6 figures Version 2: new appendix on flat connections in the 3d-3d correspondenc