1,721,019 research outputs found
Defects, nested instantons and comet-shaped quivers
Full text linkWe introduce and study a surface defect in four dimensional gauge theories
supporting nested instantons with respect to the parabolic reduction of the
gauge group at the defect. This is engineered from a D3/D7-branes system on a
non compact Calabi-Yau threefold . For ,
the product of a two torus times the cotangent bundle over a Riemann
surface with marked points, we propose an effective theory
in the limit of small volume of given as a comet shaped
quiver gauge theory on , the tail of the comet being made of a flag quiver
for each marked point and the head describing the degrees of freedom due to the
genus . Mathematically, we obtain for a single D7-brane conjectural explicit
formulae for the virtual equivariant elliptic genus of a certain bundle over
the moduli space of the nested Hilbert scheme of points on the affine plane. A
connection with elliptic cohomology of character varieties and an elliptic
version of modified Macdonald polynomials naturally arises
Seiberg-Witten theory as a Fermi gas
No full textWe explore a new connection between Seiberg–Witten theory and quantum statistical systems by relating the dual partition function of SU(2) Super Yang–Mills theory in a self-dual Ω background to the spectral determinant of an ideal Fermi gas. We show that the spectrum of this gas is encoded in the zeroes of the Painlevé III 3τ function. In addition, we find that the Nekrasov partition function on this background can be expressed as an O(2) matrix model. Our construction arises as a four-dimensional limit of a recently proposed conjecture relating topological strings and spectral theory. In this limit, we provide a mathematical proof of the conjecture for the local P1× P1 geometry
RG FLOW IRREVERSIBILITY, C THEOREM AND TOPOLOGICAL NATURE OF 4-D N=2 SYM
Full text linkWe determine the exact beta function and a RG flow Lyapunov function for N=2 super-Yang-Mills (SYM) theory with the gauge group SU(n). It turns out that the classical discriminants of the Seiberg-Witten curves determine the RG potential. The radial irreversibility of the RG flow in the SU(2) case and the nonperturbative identity relating the u modulus and the superconformal anomaly indicate the existence of a four-dimensional analogue of the c theorem for N=2 SYM theory which we formulate for the full SU(n) theory. Our investigation provides further evidence of the essentially topological nature of the theory
N=2*Gauge Theory, Free Fermions on the Torus and Painleve VI
No full textIn this paper we study the extension of Painlevé/gauge theory correspondence to circular quivers by focusing on the special case of SU(2) N= 2 ∗ theory. We show that the Nekrasov–Okounkov partition function of this gauge theory provides an explicit combinatorial expression and a Fredholm determinant formula for the tau-function describing isomonodromic deformations of SL2 flat connections on the one-punctured torus. This is achieved by reformulating the Riemann–Hilbert problem associated to the latter in terms of chiral conformal blocks of a free-fermionic algebra. This viewpoint provides the exact solution of the renormalization group flow of the SU(2) N= 2 ∗ theory on self-dual Ω -background and, in the Seiberg–Witten limit, an elegant relation between the IR and UV gauge couplings. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature
Elliptic non-Abelian Donaldson-Thomas invariants of C3
Full text linkWe compute the elliptic genus of the D1/D7 brane system in flat space, finding a non-trivial dependence on the number of D7 branes, and provide an F-theory interpretation of the result. We show that the JK-residues contributing to the elliptic genus are in one-to-one correspondence with coloured plane partitions and that the elliptic genus can be written as a chiral correlator of vertex operators on the torus. We also study the quantum mechanical system describing D0/D6 bound states on a circle, which leads to a plethystic exponential formula that can be connected to the M-theory graviton index on a multi-Taub-NUT background. The formula is a conjectural expression for higher-rank equivariant K-theoretic Donaldson-Thomas invariants on C3
Exact results for N = 2 supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants
Full text linkWe 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∗ 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. © 2016, The Author(s)
From BRST to light-cone description of higher spin gauge fields
No full textinfo:eu-repo/semantics/publishe
Quantum Hitchin Systems via β -Deformed Matrix Models
Full text linkWe study the quantization of Hitchin systems in terms of β-deformations of generalized matrix models related to conformal blocks of Liouville theory on punctured Riemann surfaces. We show that in a suitable limit, corresponding to the Nekrasov–Shatashvili one, the loop equations of the matrix model reproduce the Hamiltonians of the quantum Hitchin system on the sphere and the torus with marked points. The eigenvalues of these Hamiltonians are shown to be the ϵ1-deformation of the chiral observables of the corresponding N= 2 four dimensional gauge theory. Moreover, we find the exact wave-functions in terms of the matrix model representation of the conformal blocks with degenerate field insertions
Toda equations for surface defects in SYM and instanton counting for classical Lie groups
Full text linkThe partition function of super Yang-Mills theories with
arbitrary simple gauge group coupled to a self-dual -background is
shown to be fully determined by studying the renormalization group equations
relevant to the surface operators generating its one-form symmetries. The
corresponding system of equations results in a Toda
chain on the root system of the Langlands dual, the evolution parameter being
the RG scale. A systematic algorithm computing the full multi-instanton
corrections is derived in terms of recursion relations whose gauge theoretical
solution is obtained just by fixing the perturbative part of the IR
prepotential as its asymptotic boundary condition for the RGE. We analyse the
explicit solutions of the -system for all the classical groups at the
diverse levels, extend our analysis to affine twisted Lie algebras and provide
conjectural bilinear relations for the -functions of linear quiver gauge
theory.Comment: 34 pages + appendices, comments welcom
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