67 research outputs found
Parafermionic Liouville field theory and instantons on ALE spaces
In this paper we study the correspondence between the
coset conformal field
theories and SU(n) gauge theories on
. Namely we check the correspondence between the
SU(2) Nekrasov partition function on and the
conformal blocks of the parafermion algebra (in and modules).
We find that they are equal up to the U(1)-factor as it was in all cases of
AGT-like relations. Studying the structure of the instanton partition function
on we also find some evidence that this
correspondence with arbitrary takes place up to the U(1)-factor.Comment: 21 pages, 6 figures, misprints corrected, references added, version
to appear in JHE
Instantons and 2d Superconformal field theory
A recently proposed correspondence between 4-dimensional N=2 SUSY SU(k) gauge
theories on R^4/Z_m and SU(k) Toda-like theories with Z_m parafermionic
symmetry is used to construct four-point N=1 super Liouville conformal block,
which corresponds to the particular case k=m=2.
The construction is based on the conjectural relation between moduli spaces
of SU(2) instantons on R^4/Z_2 and algebras like \hat{gl}(2)_2\times NSR. This
conjecture is confirmed by checking the coincidence of number of fixed points
on such instanton moduli space with given instanton number N and dimension of
subspace degree N in the representation of such algebra.Comment: 13 pages, exposition improved, references adde
Directed -in vitro- evolution of Precambrian and extant Rubiscos
Rubisco is an ancient, catalytically conserved yet slow enzyme, which plays a central role in the
biosphere’s carbon cycle. The design of Rubiscos to increase agricultural productivity has hitherto
relied on the use of in vivo selection systems, precluding the exploration of biochemical traits that are
not wired to cell survival. We present a directed -in vitro- evolution platform that extracts the enzyme
from its biological context to provide a new avenue for Rubisco engineering. Precambrian and extant
form II Rubiscos were subjected to an ensemble of directed evolution strategies aimed at improving
thermostability. The most recent ancestor of proteobacteria -dating back 2.4 billion years- was uniquely
tolerant to mutagenic loading. Adaptive evolution, focused evolution and genetic drift revealed a
panel of thermostable mutants, some deviating from the characteristic trade-offs in CO2-fixing speed
and specificity. Our findings provide a novel approach for identifying Rubisco variants with improved
catalytic evolution potential.This work was supported by the REPSOL Research contracts Rubolution (RC020401120018), Rubolution 2.0 (RC
020401140042), the CSIC project PIE-201780E043 and the Australian Research Council grant CE140100015
Exact results for N = 2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants
We provide a contour integral formula for the exact partition function of N = 2 supersymmetric U(N) gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for U(2) N = 2 17 theory on CP2 for all instanton numbers. In the zero mass case, corresponding to the N = 4 supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a longstanding conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new. \ua9 2016, The Author(s)
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