In this paper I will further investigate the spectrum of quantum gravity or string theories at large number of dimensions. We will see that volumes of certain orbifolds shrink at large D. It follows that the mass spectra of the leading Kaluza-Klein towers and also of wrapped brane states on these orbifolds possess a non-trivial dependence on D: KK modes become heavy at large D, whereas wrapped branes become light. This observation can be used either to apply the Large Dimension Conjecture or, as we will do, to investigate the possibility of a D-duality symmetry, which relates in gravity compactifications of different dimensions. We will set up the general rules for D-duality in higher dimensional gravity. However due to existence of the critical dimensions, D-duality is quite restricted in string theory. As simple tests for D-duality in string theory, we will discuss the duality between M-theory on a two-dimensional orbifold, namely the Möbius strip, and an IIB S-fold on a circle, which corresponds to the heterotic CHL string, as well the duality between a (truncated) 12-dimensional theory on a three-dimensional orbifold and another IIB S-fold compactification. Finally I also comment on the possible existence of exotic theories at large D.
In this work we study F-theory on symmetric toroidal orbifolds that exhibit roto-translations, which are point group rotations accompanied by fractional lattice shifts. These geometries admit a rich class of effects, such as twisted affine folded fibers, multiple fibers, and up to three distinct torus-fibrations that yield different M/F-theory lifts. We discuss the six-dimensional physics of the F-theory lifts, which generically host superconformal subsectors and a IIB axio-dilaton fixed to strong coupling. In addition we find that these theories exhibit a rich set of p=0,1,2 discrete p-form g…
Multi-instanton and string loop corrections in toroidal orbifold models
我们分析了N=2（微扰和非微扰）的有效理论的修正，在I型orbifold模型中的双杂种优势的描述是可用的。这些修正可能在唯象情景中发挥重要作用。更精确地说，我们考虑了两个特殊的紧化：Bianchi-Sagnotti-Gimon-Polchinski轨道折叠和具有N=1超对称性和规范群SO（q）x SO（32-q）的自由作用Z_2 x Z_2轨道折叠。利用微扰计算的物理规范耦合的杂波侧，我们获得多瞬子和单圈弦修正的Kähler势和规范动力学函数的这些模型。非微扰修正表现为对相关Hecke算子的求和，而对Kähler势的单圈修正与[1，2]中提出的表达式相匹配。我们认为，这些修正是普遍的，在一类给定的模型中，目标空间的模块化不变性（或它的一个子群）举行。
Motivated by the smallness of the cosmological constant we investigate whether it is possible to have vanishing one-loop heterotic string partition functions for six-dimensional non-supersymmetric toroidal orbifolds. A straightforward way to realize this presents itself, when each orbifold sector separately preserves some Killing spinors, but none of them survives in all sectors combined. By applying some representation theory to the abstract finite point groups underlying toroidal orbifolds it turns out, that this is never possible. This leads to a nonexistence proof of locally but not global…
We consider the torus compactifications with flux of a class of $6d$ $(1,0)$ SCFTs that can be engineered as the low-energy theories on M$5$-branes near an M$9$-plane on a $C^2/Z_2$ singularity. Specifically, we concentrate on the two SCFTs where the $Z_2$ orbifold action acts non-trivially on the $E_8$ global symmetry. We analyze this problem by compactifying to $5d$, where we can exploit the relation to $5d$ duality domain walls. By a suitable guess of the domain wall theories, the resulting $4d$ theories can be conjectured. These can then be tested by comparing their properties, notably ano…
We study the modular symmetry on magnetized toroidal orbifolds with Scherk-Schwarz phases. In particular, we investigate finite modular flavor groups for three-generation modes on magnetized orbifolds. The three-generation modes can be the three-dimensional irreducible representations of covering groups and central extended groups of $Γ_N$ for $N=3,4,5,7,8,16$, that is, covering groups of $Δ(6(N/2)^2)$ for $N=$ even and central extensions of $PSL(2,\mathbb{Z}_{N})$ for $N=$odd with Scherk-Schwarz phases. We also study anomaly behaviors.
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 for the number $n_η$ of orbifold zero modes belonging to $\mathbb{Z}_{N}$ eigenvalue $η$. Since it turns out that $n_η$ quite complicatedly depends on the flux quanta $M$, the Scherk-Schwarz twist phase $(α_1, α_2)$, and the $\mathbb{Z}_{N}$ eigenvalue $η$, it seems hard that $n_η$ can be universally explained in a simple formula. We, however, succ…
