On AGT relations with surface operator insertion and a stationary limit of beta-ensembles

We present a summary of what is currently known about of the AGT relations for conformal blocks with the additional insertion of the simplest degenerate operator, and a special choice of the corresponding intermediate dimension, in which the conformal blocks satisfy hypergeometric-type differential equations in the position of the degenerate operator. Special attention is devoted to the representation of the conformal block through using the beta-ensemble resolvents and to its asymptotics in the limit of large dimensions (both external and intermediate) taken asymmetrically in terms of the deformation epsilon-parameters. The next-to-leading term in the asymptotics defines the generating differential in the Bohr–Sommerfeld representation of the one-parameter deformed Seiberg–Witten prepotentials, (whose full two-parameter deformation leads to Nekrasov functions). This generating differential is also shown to be the one-parameter version of the single-point resolvent for the corresponding beta-ensemble, and its periods in the perturbative limit of the gauge theory are expressed through the ratios of the Harish–Chandra function. The Schrödinger/Baxter equations, considered earlier in this context, directly follow from the differential equations for the degenerate conformal block. This approach provides a powerful method for the evaluation of the single-deformed prepotentials, and even for the Seiberg–Witten prepotentials themselves. We primarily concentrate on the representative case of the insertion into the four-point block on a sphere and the one-point block on a torus.     

Proving AGT conjecture as HS duality: Extension to five dimensions

We extend the proof from Mironov et al. (2011) [25], which interprets the AGT relation as the Hubbard-Stratonovich duality relation to the case of 5d gauge theories. This involves an additional q-deformation. Not surprisingly, the extension turns out to be straightforward: it is enough to substitute all relevant numbers by q-numbers in all the formulas, Dotsenko-Fateev integrals by the Jackson sums and the Jack polynomials by the MacDonald ones. The problem with extra poles in individual Nekrasov functions continues to exist, therefore, such a proof works only for β=1, i.e. for q=t in MacDonald?s notation. For β≠1 the conformal blocks are related in this way to a non-Nekrasov decomposition of the LMNS partition function into a double sum over Young diagrams.     

Construction of AFLT States by Reflection Method and Recursion Formula

The AFLT states ｜P〉Y1,Y2 has reflection symmetry, S^n｜P〉Y1,Y2 = ｜- P〉Y2,Y2, nb =-2P, where S is the screening charge. AFLT state can be constructed using this reflect symmetry. We propose a recursion formula for this construction. The recursion formula is factorized completely.     

The Dysregulation of the Renin–Angiotensin System in COVID-19 Studied by Serum Proteomics: Angiotensinogen Increases with Disease Severity

(1) Background: ACE and CPN serum activity correlated with disease severity in an earlier study of 45 hospitalized COVID-19 patients. The serum protein profile was investigated in the same cohort here to shed more light on the involvement of the renin–angiotensin system (RAS). (2) Methods: High-definition mass spectrometry-based protein expression analysis was performed, followed by multivariate statistical and network analyses. (3) Results: The protein profiles of hospitalized patients (HoP) differed significantly from those of convalescent and healthy probands. Surprisingly, HoP samples separated into six groups according to their protein profiles: group (G) 1 represented the youngest and the least afflicted patients, and G6 the oldest and critically ill patients. At least two major pathophysiological schemes were indicated based on differing involvement of the kallikrein-kinin system (KKS), the RAS and complement activation. The serum angiotensinogen concentration increased with disease severity. (4) Conclusions: The important role of the RAS in the response to COVID-19 infection was substantiated, but other pathways such as the KKS, plasminogen activation and complement activation influence the systemic response to the infection.     

Synthesis and preliminary biological evaluation of the derivatives of O6-benzylguanine as inactivators of O6-alkylguanine-DNA alkyltransferase

A series of new O6-BG derivatives （14-21,23-30） were synthesized as inactivators of O6-Alkylguanine-DNA alkyltransferase （AGT）, and their ability to inhibit AGT was preliminary evaluated by MTT with O6-BG as the control. The result suggested compound 30 displayed a higher activity than O6-BG.     

N-(2-氯乙基)-N'-2-(O~6-苄基-9-鸟嘌呤基)乙基-N-亚硝基脲的合成

以O~6-苄基鸟嘌呤为原料,经取代反应和盖布瑞尔反应制得N9-(2-胺基)乙基-O6-苄基鸟嘌呤(4);4与异氰酸酯经取代反应和经亚硝化反应合成了N-(2-氯乙基)-N'-2-(O6-苄基-9-鸟嘌呤基)乙基-N-亚硝基脲(6)。4和6为新化合物,其结构经UV-Vis,1H NMR,13C NMR,IR和HR-ESI-MS表征。     

Construction of AFLT States for W_NH Symmetry,Analytic Continuation and Integrability on AGT Relation

We propose a Hamiltonian to the construction of the AFLT states for WNsymmetry. We generalize the AGT relation to generic(extended) conformal field theory with 1 ≤ c ∞. We analyze the triangular structure hidden in the AGT relation with WNsymmetry in detail and the triangular structure implies the integrability.     

Check of AGT relation for conformal blocks on sphere

The AGT conjecture identifying conformal blocks with the Nekrasov functions is investigated for the spherical conformal blocks with more than 4 external legs. The diagram technique which arises in conformal block calculation involves propagators and vertices. We evaluated vertices with two Virasoro algebra descendants and explicitly checked the AGT relation up to the third order of the expansion for the 5-point and 6-point conformal blocks on sphere confirming all the predictions of arXiv:0906.3219 relevant in this situation. We propose that U(1)$U(1)$-factor can be extracted from the matrix elements of the free field vertex operators. We studied the n-point case, and found out that our results confirm the AGT conjecture up to the third order expansions.