ترغب بنشر مسار تعليمي؟ اضغط هنا

Mordell integrals and Giveon-Kutasov duality

164   0   0.0 ( 0 )
 نشر من قبل Georgios Giasemidis Dr
 تاريخ النشر 2015
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

We solve, for finite $N$, the matrix model of supersymmetric $U(N)$ Chern-Simons theory coupled to $N_{f}$ massive hypermultiplets of $R$-charge $frac{1}{2}$, together with a Fayet-Iliopoulos term. We compute the partition function by identifying it with a determinant of a Hankel matrix, whose entries are parametric derivatives (of order $N_{f}-1$) of Mordell integrals. We obtain finite Gauss sums expressions for the partition functions. We also apply these results to obtain an exhaustive test of Giveon-Kutasov (GK) duality in the $mathcal{N}=3$ setting, by systematic computation of the matrix models involved. The phase factor that arises in the duality is then obtained explicitly. We give an expression characterized by modular arithmetic (mod 4) behavior that holds for all tested values of the parameters (checked up to $N_{f}=12$ flavours).



قيم البحث

اقرأ أيضاً

170 - Mykola Dedushenko 2018
We review some aspects of the cutting and gluing law in local quantum field theory. In particular, we emphasize the description of gluing by a path integral over a space of polarized boundary conditions, which are given by leaves of some Lagrangian f oliation in the phase space. We think of this path integral as a non-local $(d-1)$-dimensional gluing theory associated to the parent local $d$-dimensional theory. We describe various properties of this procedure and spell out conditions under which symmetries of the parent theory lead to symmetries of the gluing theory. The purpose of this paper is to set up a playground for the companion paper where these techniques are applied to obtain new results in supersymmetric theories.
234 - Enrico Olivucci 2021
In this paper we consider a conformal invariant chain of $L$ sites in the unitary irreducible representations of the group $SO(1,5)$. The $k$-th site of the chain is defined by a scaling dimension $Delta_k$ and spin numbers $frac{ell_k}{2}$, $frac{do t{ell}_k}{2}$. The model with open and fixed boundaries is shown to be integrable at the quantum level and its spectrum and eigenfunctions are obtained by separation of variables. The transfer matrices of the chain are graph-builder operators for the spinning and inhomogeneous generalization of squared-lattice fishnet integrals on the disk. As such, their eigenfunctions are used to diagonalize the mirror channel of the the Feynman diagrams of Fishnet conformal field theories. The separated variables are interpreted as momentum and bound-state index of the $textit{mirror excitations}$ of the lattice: particles with $SO(4)$ internal symmetry that scatter according to an integrable factorized $mathcal{S}$-matrix in $(1+1)$ dimensions.
We conjecture the quantum analogue of the classical trace formulae for the integrals of motion of the quantum hyperbolic Ruijsenaars-Schneider model. This is done by departing from the classical construction where the corresponding model is obtained from the Heisenberg double by the Poisson reduction procedure. We also discuss some algebraic structures associated to the Lax matrix in the classical and quantum theory which arise upon introduction of the spectral parameter.
We compute characteristic numbers of elliptically fibered fourfolds with multisections or non-trivial Mordell-Weil groups. We first consider the models of type E$_{9-d}$ with $d=1,2,3,4$ whose generic fibers are normal elliptic curves of degree $d$. We then analyze the characteristic numbers of the $Q_7$-model, which provides a smooth model for elliptic fibrations of rank one and generalizes the E$_5$, E$_6$, and E$_7$-models. Finally, we examine the characteristic numbers of $G$-models with $G=text{SO}(n)$ with $n=3,4,5,6$ and $G=text{PSU}(3)$ whose Mordell-Weil groups are respectively $mathbb{Z}/2mathbb{Z}$ and $mathbb{Z}/3 mathbb{Z}$. In each case, we compute the Chern and Pontryagin numbers, the Euler characteristic, the holomorphic genera, the Todd-genus, the L-genus, the A-genus, and the eight-form curvature invariant from M-theory.
Whenever available, refined BPS indices provide considerably more information on the spectrum of BPS states than their unrefined version. Extending earlier work on the modularity of generalized Donaldson-Thomas invariants counting D4-D2-D0 brane boun d states in type IIA strings on a Calabi-Yau threefold $mathfrak{Y}$, we construct the modular completion of generating functions of refined BPS indices supported on a divisor class. Although for compact $mathfrak{Y}$ the refined indices are not protected, switching on the refinement considerably simplifies the construction of the modular completion. Furthermore, it leads to a non-commutative analogue of the TBA equations, which suggests a quantization of the moduli space consistent with S-duality. In contrast, for a local CY threefold given by the total space of the canonical bundle over a complex surface $S$, refined BPS indices are well-defined, and equal to Vafa-Witten invariants of $S$. Our construction provides a modular completion of the generating function of these refined invariants for arbitrary rank. In cases where all reducible components of the divisor class are collinear (which occurs e.g. when $b_2(mathfrak{Y})=1$, or in the local case), we show that the holomorphic anomaly equation satisfied by the completed generating function truncates at quadratic order. In the local case, it agrees with an earlier proposal by Minahan et al for unrefined invariants, and extends it to the refined level using the afore-mentioned non-commutative structure. Finally, we show that these general predictions reproduce known results for $U(2)$ and $U(3)$ Vafa-Witten theory on $mathbb{P}^2$, and make them explicit for $U(4)$.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا