185 research outputs found

    Spectral Duality Between Heisenberg Chain and Gaudin Model

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    In our recent paper we described relationships between integrable systems inspired by the AGT conjecture. On the gauge theory side an integrable spin chain naturally emerges while on the conformal field theory side one obtains some special reduced Gaudin model. Two types of integrable systems were shown to be related by the spectral duality. In this paper we extend the spectral duality to the case of higher spin chains. It is proved that the N-site GL(k) Heisenberg chain is dual to the special reduced k+2-points gl(N) Gaudin model. Moreover, we construct an explicit Poisson map between the models at the classical level by performing the Dirac reduction procedure and applying the AHH duality transformation.Comment: 36 page

    Spectral Duality in Integrable Systems from AGT Conjecture

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    We describe relationships between integrable systems with N degrees of freedom arising from the AGT conjecture. Namely, we prove the equivalence (spectral duality) between the N-cite Heisenberg spin chain and a reduced gl(N) Gaudin model both at classical and quantum level. The former one appears on the gauge theory side of the AGT relation in the Nekrasov-Shatashvili (and further the Seiberg-Witten) limit while the latter one is natural on the CFT side. At the classical level, the duality transformation relates the Seiberg-Witten differentials and spectral curves via a bispectral involution. The quantum duality extends this to the equivalence of the corresponding Baxter-Schrodinger equations (quantum spectral curves). This equivalence generalizes both the spectral self-duality between the 2x2 and NxN representations of the Toda chain and the famous AHH duality

    S-duality as a beta-deformed Fourier transform

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    An attempt is made to formulate Gaiotto's S-duality relations in an explicit quantitative form. Formally the problem is that of evaluation of the Racah coefficients for the Virasoro algebra, and we approach it with the help of the matrix model representation of the AGT-related conformal blocks and Nekrasov functions. In the Seiberg-Witten limit, this S-duality reduces to the Legendre transformation. In the simplest case, its lifting to the level of Nekrasov functions is just the Fourier transform, while corrections are related to the beta-deformation. We calculate them with the help of the matrix model approach and observe that they vanish for beta=1. Explicit evaluation of the same corrections from the U_q(sl(2)) infinite-dimensional representation formulas due to B.Ponsot and J.Teshner remains an open problem.Comment: 21 page

    Provision of Epidemiological Welfare on Plague under Aggravation of Epizootic Situation in the Pre-Caspian Sandy Natural Plague Focus in 2014

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    Reviewed are the lessons learned from cooperation between Rospotrebnadzor institutions in the provision of epidemiological welfare on plague under aggravation of epizootic situation in the territory of the Pre-Caspian sandy natural plague focus in 2014. Plague control measures combined epizootiological and epidemiological monitoring, specific and non-specific prophylaxis, training activities for medical and veterinary officers, instructional advice for medical facilities on matters of infection prevention, and sensitization campaign. Furthermore, vaccinated against plague were 4460 people, field disinsection over 50.5 km2 area was performed, as well as field deratization - 89.4 km2, township disinsection - 257.3 thous. m2, and township deratization - 329.1 thous. m2. Financial expenses on prophylactic (anti-epidemic) activities amounted to 23265.8 thousand rubles. Outlined was viability of preventive planning and prophylactic measures in the territories with forecasted aggravation of epizootic situation in natural plague foci of the Russian Federation

    Deformed planar topological open string amplitudes on Seiberg-Witten curve

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    We study refined B-model via the beta ensemble of matrix models. Especially, for four dimensional N=2 SU(2) supersymmetric gauge theories with N_f=0,1 and 2 fundamental flavors, we discuss the correspondence between deformed disk amplitudes on each Seiberg-Witten curve and the Nekrasov-Shatashvili limit of the corresponding irregular one point block of a degenerate operator via the AGT correspondence. We also discuss the relation between deformed annulus amplitudes and the irregular two point block of the degenerate operator, and check a desired agreement for N_f=0 and 1 cases.Comment: 27 pages. v2: minor changes and references added. v3: minor corrections and one reference adde

    Enhancement of Epidemiological Surveillance in Natural Plague Foci of the Russian Federation and Forecast of Epizootic Activity for 2022

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    The aim of the research was to assess epizootic activity of natural plague foci in the Russian Federation in 2021 and provide a prognosis for 2022. Activation of epizootic process has been detected in Central-Caucasian high-mountain natural plague focus after a recess since 2007. Local epizootics persist to develop in Tuva Mountain and Gorno-Altai highmountain plague foci. Total area of epizooties in Russia in 2021 amounted to 1649.5 km2. 28 plague microbe strains were isolated. Animals infected with plague were not found in Tersko-Sunzhensky low-mountain, Dagestan plain-piedmont, Precaspian north-western steppe, Volga-Ural steppe, Trans-Baikal steppe, Volga-Ural sandy, Caspian sandy and EastCaucasian high-mountain natural plague foci. It is demonstrated that epidemiological welfare as regards plague in Russia in 2017–2021 was achieved through annual epizootic monitoring of plague-enzootic territories, timely epizooty detection and preventive activities aimed at reducing the risk of infection. Substantiated has been the forecast for tense epidemiological situation on the territory of Karachay-Cherkessia, Kabardino-Balkaria, Altai Republic and Tuva Republic in 2022. A new Epitracker application has been proven to be prospective for rapid assessment of actual epidemiological situation in natural plague foci

    Epizootic Activity of Natural Plague Foci of the Russian Federation in 2015, and Prognosis for 2016

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    Objective of the study is to evaluate the state of parasitic systems and activity of natural plague foci of the Russian Federation in 2015 and to develop epizootiological forecast for 2016. In 2015, plague epizooties were detected in the territory of Gorno-Altaisk high-mountain, Tuva mountain, and Pre-Caspian sandy natural plague foci with a total area amounting to 1573.4 square kilometers. Isolated were 46 strains of plague microbe, including the isolates from rodents and leporines - 18, and from fleas - 28. Substantiated is epizootiological prognosis for sustaining challenging epidemiological situation in Gorno-Altaisk high-mountain and Tuva mountain natural foci in 2016. Demonstrated is the fact that consequently to effective prompt prophylactic measures (field deratization, disinsection) in 2015 decreased epizootic activity of Pre-Caspian sandy focus is observed. Specified is retention of low numbers of carriers and vectors of plague in natural foci of North and North-Western Caspian Sea Region, Pre-Caucasian, Caucasian, and Transbaikal Territories. Identified is upward trend for numbers of the little souslik in Pre-Caspian North-Western steppe, Volga-Ural steppe, Dagestan lowland-piedmont, and Pre-Caspian sandy natural plague foci

    EPIZOOTIC ACTIVITY OF NATURAL PLAGUE FOCI IN THE RUSSIAN FEDERATION IN 2016, AND PROGNOSIS FOR 2017

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    Objective of the study was to evaluate the state of parasitic systems and activity of the natural plague foci of the Russian Federation in 2016 and to develop epizootiological forecasting for 2017. In 2016 epizooties of plague were registered in the territory of the KoshAgach District of the Altai Republic and Mongun-Taiginsky, Ovyursky, and Tes-Khemsky Kozhuuns of the Republic of Tyva. The total area coverage was 1692.6 km2. Isolated were 87 strains of plague microbe, including the isolates from rodents and lagomorphs – 31, from fleas – 47, lice – 7, and Ixodidae ticks – 2. Verified has been epizootiological forecast for the year 2017, which shows that epidemiological situation will remain tense. In order to reduce the epidemic risks, comprehensive plans of preventive activities have been developed. In the territory of the other natural foci epizootic manifestations of plague are not expected to occur. Only in PreCaspian sandy focus, situated in the territory of Lagan and Chernozemelsky Regions of the Kalmyk Republic, probability of the singly infected animal findings during the autumn season, 2017 is retained

    q-Virasoro Modular Double and 3d Partition Functions

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