496 research outputs found
NONPERTURBATIVE RENORMALIZATION GROUP EQUATION AND BETA FUNCTION IN N=2 SUSY YANG-MILLS
No full textWe obtain the exact beta function for N = 2 supersymmetric SU Yang-Mills theory and prove the nonperturbative renormalization group equation ∂ΛF = ∂Λ0F×exp[-2τ0τdxβ-1]
NONPERTURBATIVE RELATIONS IN N=2 SUSY YANG-MILLS AND WDVV EQUATION
No full textWe find the nonperturbative relation between , the prepotential F and in N = 2 supersymmetric Yang-Mills theory (SYM) with gauge group SU(3). Nonlinear differential equations for F including the Witten-Dijkgraaf-Verlinde-Verlinde equation are obtained, indicating that N = 2 SYM theories are essentially topological field theories which should be seen as the low-energy limit of some topological string theory. Furthermore, we construct relevant modular invariant quantities, derive canonical relations between the periods, and find the β function in terms of the moduli. In doing this we discuss the uniformization problem for the quantum moduli space
Singular Spin Structures and Superstrings
No full textThere are two main problems in finding the higher genus superstring measure.
The first one is that for the super moduli space is not projected.
Furthermore, the supermeasure is regular for , a bound related to the
source of singularities due to the divisor in the moduli space of Riemann
surfaces with even spin structure having holomorphic sections, such a divisor
is called the -null divisor. A result of this paper is the
characterization of such a divisor. This is done by first extending the Dirac
propagator, that is the Szeg\"o kernel, to the case of an arbitrary number of
zero modes, that leads to a modification of the Fay trisecant identity, where
the determinant of the Dirac propagators is replaced by the product of two
determinants of the Dirac zero modes. By taking suitable limits of points on
the Riemann surface, this {\it holomorphic Fay trisecant identity} leads to
identities that include points dependent rank 3 quadrics in .
Furthermore, integrating over the homological cycles gives relations for the
Riemann period matrix which are satisfied in the presence of Dirac zero modes.
Such identities characterize the -null divisor. Finally, we provide the
geometrical interpretation of the above points dependent quadrics and shows,
via a new -identity, its relation with the Andreotti-Mayer quadric.Comment: 18 page
N=2 SYM RG SCALE AS MODULUS FOR WDVV EQUATIONS
No full textWe derive a new set of Witten-Dijkgraaf-Verlinde-Verlinde equations for N=2 SYM theory in which the renormalization scale Λ is identified with the distinguished modulus which naturally arises in topological field theories
BETA FUNCTION, C THEOREM AND WDVV EQUATIONS IN 4-D N=2 SYM
No full textWe show that the exact beta-function of 4D N=2 SYM plays the role of the metric whose inverse satisfies the WDVV-like equations FiklβlmFmnj=FjklβlmFmni. The conjecture that the WDVV-like equations are equivalent to the identity involving the u-modulus and the prepotential F, seen as a superconformal anomaly, sheds light on the recently considered c-theorem for the N=2 SYM field theories
INSTANTONS AND RECURSION RELATIONS IN N=2 SUSY GAUGE THEORY
No full textWe find the transformation properties of the prepotential F of N = 2 SUSY gauge theory with gauge group SU(2). Next we show that G(a) = πi(F(a) -1/2a ∂aF(a)) is modular invariant. We also show that u = G(a), so that F() =1/πi + 1/2. This implies thatG (a) satisfies the non-linear differential equation (1 - G2) G'' +1/4aG '3 = 0. We use this equation to derive recursion relations for the instanton contributions. These results can be extended to more general cases
Exponentiating Higgs
No full textWe consider two related formulations for mass generation in the U(1) Higgs–Kibble model and in the
Standard Model (SM). In the first formulation there are no scalar self-interactions and, in the case of
the SM, the formulation is related to the normal subgroup of G = SU(3) × SU(2) × U(1), generated by
(e2πi/3 I,−I, eπi/3) ∈ G, that acts trivially on all the fields of the SM. The key step of our construction
is to relax the non-negative definiteness condition for the Higgs field due to the polar decomposition.
This solves several stringent problems, that we will shortly review, both at the non-perturbative and
perturbative level. We will show that the usual polar decomposition of the complex scalar doublet
should be done with U ∈ SU(2)/Z2 S O(3), where Z2 is the group generated by −I, and with the Higgs
field φ ∈ R rather than φ ∈ R≥0. As a byproduct, the investigation shows how Elitzur theorem may be
avoided in the usual formulation of the SM. It follows that the simplest lagrangian density for the Higgs
mechanism has the standard kinetic term in addition to the mass term, with the right sign, and to a linear
term in φ. The other model concerns the scalar theories with normal ordered exponential interactions.
The remarkable property of these theories is that for D > 2 the purely scalar sector corresponds to a free
theory
SOLVING N=2 SYM BY REFLECTION SYMMETRY OF QUANTUM VACUA
No full textThe recently rigorously proved nonperturbative relation u=πi(F-a∂aF/2), underlying N=2 supersymmetry Yang-Mills theory with the gauge group SU(2), implies both the reflection symmetries u(τ) ̄=u(-τ ̄) and u(τ+1)=-u(τ) which hold exactly. The relation also implies that τ is the inverse of the uniformizing coordinate u of the moduli space of quantum vacua MSU(2), that is, τ:MSU(2)-->H, where H is the upper half plane. In this context, the above quantum symmetries are the key points to determine MSU(2). It turns out that the functions a(u) and aD(u), which we derive from first principles, actually coincide with the solution proposed by Seiberg and Witten. We also consider some relevant generalizations
Determinantal Characterization of Canonical Curves and Combinatorial Theta Identities
No full textWe characterize genus g canonical curves by the vanishing of combinatorial products of g + 1 determinants of Brill-Noether matrices. This also implies the characterization of canonical curves in terms of (g−2)(g−3)/2 theta identities. A remarkable mechanism, based on a basis of H^0(K_C ) expressed in terms of Szegö kernels, reduces such identities to a simple rank condition for matrices whose entries are logarithmic derivatives of theta functions. Such a basis, together with the Fay trisecant identity, also leads to the solution of the question of expressing the determinant of Brill-Noether matrices in terms of theta functions, without using the problematic Klein-Fay section σ
RG FLOW IRREVERSIBILITY, C THEOREM AND TOPOLOGICAL NATURE OF 4-D N=2 SYM
No full textWe 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
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