اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدModular symmetry and zeros in magnetic compactifications
100
0
0.0
(
0
)
تأليف
Yoshiyuki Tatsuta
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We discuss the modular symmetry and zeros of zero-mode wave functions on two-dimensional torus $T^2$ and toroidal orbifolds $T^2/mathbb{Z}_N$ ($N=2,3,4,6$) with a background homogeneous magnetic field. As is well-known, magnetic flux contributes to the index in the Atiyah-Singer index theorem. The zeros in magnetic compactifications therefore play an important role, as investigated in a series of recent papers. Focusing on the zeros and their positions, we study what type of boundary conditions must be satisfied by the zero modes after the modular transformation. The consideration in this paper justifies that the boundary conditions are common before and after the modular transformation.
قيم البحث
اقرأ أيضاً
We thoroughly analyze the number of independent zero modes and their zero points on the toroidal orbifold $T^2/mathbb{Z}_N$ ($N = 2, 3, 4, 6$) with magnetic flux background, inspired by the Atiyah-Singer index theorem. We first show a complete list f
or the number $n_{eta}$ of orbifold zero modes belonging to $mathbb{Z}_{N}$ eigenvalue $eta$. Since it turns out that $n_{eta}$ quite complicatedly depends on the flux quanta $M$, the Scherk-Schwarz twist phase $(alpha_1, alpha_2)$, and the $mathbb{Z}_{N}$ eigenvalue $eta$, it seems hard that $n_{eta}$ can be universally explained in a simple formula. We, however, succeed in finding a single zero-mode counting formula $n_{eta} = (M-V_{eta})/N + 1$, where $V_{eta}$ denotes the sum of winding numbers at the fixed points on the orbifold $T^2/mathbb{Z}_N$. The formula is shown to hold for any pattern.
We study modular symmetry anomalies in four-dimensional low-energy effective field theory, which is derived from six-dimensional supersymmetric $U(N)$ Yang-Mills theory by magnetic flux compactification. The gauge symmetry $U(N)$ is broken to $U(N_a)
times U(N_b)$ by magnetic fluxes. It is found that Abelian subgroup of the modular symmetry corresponding to discrete part of $U(1)$ can be anomalous, but other elements independent of $U(1)$ in the modular symmetry are always anomaly-free.
We derive global constraints on the non-BPS sector of supersymmetric 2d sigma-models whose target space is a Calabi-Yau manifold. When the total Hodge number of the Calabi-Yau threefold is sufficiently large, we show that there must be non-BPS primar
y states whose total conformal weights are less than 0.656. Moreover, the number of such primary states grows at least linearly in the total Hodge number. We discuss implications of these results for Calabi-Yau geometry.
We construct non-geometric compactifications by using the F-theory dual of the heterotic string compactified on a two-torus, together with a close connection between Siegel modular forms of genus two and the equations of certain K3 surfaces. The modu
lar group mixes together the Kahler, complex structure, and Wilson line moduli of the torus yielding weakly coupled heterotic string compactifications which have no large radius interpretation.
Intersecting D-brane models and their T-dual magnetic compactifications provide an attractive framework for particle physics, allowing for chiral fermions and supersymmetry breaking. Generically, magnetic compactifications have tachyons that are usua
lly removed by Wilson lines. However, quantum corrections prevent local minima for Wilson lines. We therefore study tachyon condensation in the simplest case, the magnetic compactification of type I string theory on a torus to eight dimensions. We find that tachyon condensation restores supersymmetry, which is broken by the magnetic flux, and we compute the mass spectrum of vector- and hypermultiplets. The gauge group $text{SO}(32)$ is broken to $text{USp}(16)$. We give arguments that the vacuum reached by tachyon condensation corresponds to the unique 8d superstring theory already known in the literature, with discrete $B_{ab}$ background or, in the T-dual version, the type IIB orientifold with three $text{O}7_-$-planes, one $text{O}7_+$-plane and eight D7-branes coincident with the $text{O}7_+$-plane. The ground state after tachyon condensation is supersymmetric and has no chiral fermions.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
