Hiroyuki Abe, Tatsuo Kobayashi, Hiroshi Ohki
We study (4+2n)-dimensional N=1 super Yang-Mills theory on the orbifold background with non-vanishing magnetic flux. In particular, we study zero-modes of spinor fields. The flavor structure of our models is different from one in magnetized torus models, and would be interesting in realistic model building.
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We study magnetized orbifold models. We assume the localized Fayet-Iliopoulos terms and the corresponding gauge background. Such terms lead to strong localization of zero-mode wavefunc- tions. In this setup, we compute quark mass matrices.
We study orbifolding by the $\mathbb{Z}_2^{\rm (per)}$ permutaion of $T^2_1 \times T^2_2$ with magnetic fluxes and its twisted orbifolds. We classify the possible three generation models which lead to non-vanishing Yukawa couplings on the magnetized $T^2_1 \times T^2_2$ and orbifolds including the $\mathbb{Z}_2^{\rm (per)}$ permutation and $\mathbb{Z}_2^{\rm (t)}$ twist. We also study the modular symmetry on such orbifold models. As an illustrating model, we examine the realization of quark masses and mixing angles.
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 study three generation models in the four-dimensional spacetime, which can be derived from the ten-dimensional N=1 super Yang-Mills theory on the orbifold background with a non-vanishing magnetic flux. We classify the flavor structures and show possible patterns of Yukawa matrices. Some examples of numerical studies are also shown.
We give an alternative description of the Schoen manifold as the blow-up of a Z2xZ2 orbifold in which one Z2 factor acts as a roto-translation. Since for this orbifold the fixed tori are only identified in pairs but not orbifolded, four-dimensional chirality can never be obtained in heterotic string compactifications using standard techniques alone. However, chirality is recovered when its tori become magnetized. To exemplify this, we construct an E8xE8' heterotic SU(5) GUT on the Schoen manifold with Abelian gauge fluxes, which becomes an MSSM with three generations after an appropriate Wilso…
We study of fermion zero-modes on magnetized $T^6/\mathbb{Z}_N$ orbifolds. In particular, we focus on non-factorizable orbifolds, i.e. $T^6/\mathbb{Z}_7$ and $T^6/\mathbb{Z}_{12}$ corresponding to $SU(7)$ and $E_6$ Lie lattices respectively. The number of degenerated zero-modes corresponds to the generation number of low energy effective theory in four dimensional space-time. We find that three-generation models preserving 4D $\mathcal{N}=1$ supersymmetry can be realized by magnetized $T^6/\mathbb{Z}_{12}$, but not by $T^6/\mathbb{Z}_7$. We use $Sp(6,\mathbb{Z})$ modular transformation for the…
We study the structure of Yukawa matrices derived from the supersymmetric Yang-Mills theory on magnetized orbifolds, which can realize the observed quark and charged lepton mass ratios as well as the CKM mixing angles, even with a small number of tunable parameters and without any critical fine-tuning. As a reason behind this, we find that the obtained Yukawa matrices possess a Froggatt-Nielsen like structure with Gaussian hierarchies, which provides a suitable texture for them favored by the experimental data.
We study supersymmetric (SUSY) models derived from the ten-dimensional SUSY Yang- Mills theory compactified on magnetized orbifolds, with nonvanishing Fayet-Iliopoulos (FI) terms induced by magnetic fluxes in extra dimensions. Allowing the presence of FI-terms relaxes a constraint on flux configurations in SUSY model building based on magnetized backgrounds. In this case, charged fields develop their vacuum expectation values (VEVs) to cancel the FI-terms in the D-flat directions of fluxed gauge symmetries, which break the gauge symmetries and lead to a SUSY vacuum. Based on this idea, we prop…
We construct several dynamical supersymmetry breaking (DSB) models within a single ten-dimensional supersymmetric Yang-Mills (SYM) theory, compactified on magnetized tori with or without orbifolding. We study the case that the supersymmetry breaking is triggered by a strong dynamics of $SU(N_C)$ SYM theory with $N_F$ flavors contained in the four-dimensional effective theory. We show several configurations of magnetic fluxes and orbifolds, those potentially yield, below the compactification scale, the field contents and couplings required for triggering DSB. We especially find a class of self-…
We study the modular symmetry anomaly in magnetized orbifold models. The non-perturbative effects such as D-brane instanton effects can break tree-level symmetry. We study which part of the modular symmetry is broken explicitly by Majorana mass terms with three generations of neutrinos. The modular weight of neutrino mass terms does not match with other coupling terms in tree-level Lagrangian. In addition, the $Z_N$ symmetry of the modular flavor symmetry is broken and a certain normal subgroup of the modular flavor symmetry remains in neutrino mass terms.
Magnetized orbifolds play an important role in compactifications of string theories and higher-dimensional field theories to four dimensions. Magnetic flux leads to chiral fermions, it can be a source of supersymmetry breaking and it is an important ingredient of moduli stabilization. Flux quantization on orbifolds is subtle due to the orbifold singularities. Generically, Wilson line integrals around these singularities are non-trivial, which can be interpreted as localized flux. As a consequence, flux densities on orbifolds can take the same values as on tori. We determine the transition func…
As the effective field theory of the superstring theory, ten-dimensional ${\cal N}=1$ supersymmetric Yang-Mills theory is induced. We consider the ten-dimensional space-time ${\cal M}_{10}$ as direct products of our four-dimensional space-time ${\cal M}_{4}$ and three two-dimensional compact spaces $X_i\ (i=1,2,3)$, i.e. ${\cal M}_{10} = {\cal M}_4 \times X_2 \times X_2 \times X_3$. In particular, we consider $X_i$ as a torus, the torus orbifold, and also the blow-up manifold of the torus orbifold with background magnetic fluxes. We discuss the modular symmetry in the magnetized torus and its …
We classify the combinations of parameters which lead three generations of quarks and leptons in the framework of magnetized twisted orbifolds on $T^2/Z_2$, $T^2/Z_3$, $T^2/Z_4$ and $T^2/Z_6$ with allowing nonzero discretized Wilson line phases and Scherk-Schwarz phases. We also analyze two actual examples with nonzero phases leading to one-pair Higgs and five-pair Higgses and discuss the difference from the results without nonzero phases studied previously.
We study constructions and classifications of three-generation models based on magnetized $T^4$ and $T^4/{Z}_2$ orbifold as candidates of the compact space. We focus on chiral fermion zero-mode wave functions in the extra dimensions. Freedoms of constant gauge fields, called Scherk-Schwarz phases are taken into account. Infinite number of three-generation models are yielded, corresponding to the ways in which the magnetic flux can be turned on. We classify them in a systematic manner, clarifying the relationship between different models. The Higgs sector is also studied by analyzing possible a…
We discuss an effective way for analyzing the system on the magnetized twisted orbifolds in operator formalism, especially in the complicated cases $T^{2}/Z_{3}$, $T^{2}/Z_{4}$ and $T^{2}/Z_{6}$. We can obtain the exact and analytical results which can be applicable for any larger values of the quantized magnetic flux M, and show that the (non-diagonalized) kinetic terms are generated via our formalism and the number of the surviving physical states are calculable in a rigorous manner by simply following usual procedures in linear algebra in any case. Our approach is very powerful when we try …
We consider magnetized orbifolds, where the supersymmetric mass term for a pair of up- and down-type Higgs (super)fields, called $μ$-term, is localized at the orbifold fixed points, and study the effects on the zero-mode spectra. The zero-mode degeneracy to be identified as the generation in four-dimensional (4D) effective theories is determined by the magnetic fluxes. It is known that multiple Higgs zero-modes appear in general in magnetized orbifold models. We derive the analytic form of the $μ$-term matrix in the 4D effective theory generated by the localized sources on $T^2/Z_2$ orbifold f…
Number of zero-modes on magnetized $T^4/Z_N$ orbifolds analyzed by modular transformation
该研究利用$Sp(4,\n\b{Z})$模变换分析带背景磁通量的$T^4/Z_N$轨形上的费米子零模数量，明确三代模型实现条件，并通过紧致空间宇称变换深化正负手征波函数关系的理解。
We study quark mass matrices derived from magnetized $T^2/\mathbb{Z}_2$ orbifold models. Yukawa matrices at three modular fixed points, $τ=i, e^{2πi/3}$ and $i\infty$ are invariant under $S$, $ST$ and $T$-transformations. We study these invariances on $T^2/\mathbb{Z}_2$ twisted orbifold. We find that Yukawa matrices have a kind of texture structures although ones at $τ=i\infty$ are not realistic. We classify Yukawa textures at $τ=i$ and $e^{2πi/3}$. Moreover we investigate the conditions such that quark mass matrix constructed by Yukawa textures becomes approximately rank one matrix, which is …
We study Majorana neutrino masses induced by D-brane instanton effects in magnetized orbifold models. We classify possible cases, where neutrino masses can be induced. Three and four generations are favored in order to generate neutrino masses by D-brane instantons. Explicit mass matrices have specific features. Their diagonalizing matrices correspond to the bimaximal mixing matrix in the case with even magnetic fluxes, independently of the modulus value $τ$. On the other hand, for odd magnetic fluxes, diagonalizing matrices correspond nearly to the tri-bimaximal mixing matrix near $τ=i$, whil…
We discuss the flavor structure in a resolutions of magnetized $T^2/\mathbb{Z}_2$ orbifold models. The flavor structure of Yukawa couplings among chiral zero-modes is sensitive to radii of the resolved fixed points of $T^2/\mathbb{Z}_2$ orbifold. We show in concrete models that the realistic mass hierarchy and mixing angles of the quark sector can be realized at certain values of blow-up radii, where the number of parameters in the blow-up model can be smaller than toroidal orbifold one.
Modular symmetry in magnetized $T^{2g}$ torus and orbifold models
本文研究磁化$T^{2g}$环面与轨形模型中的模对称性，按磁通矩阵分类剩余对称性，并揭示波函数及4D手征场在metaplectic同余子群下的非平凡变换性质。
We study the modular symmetry of zero-modes on $T_1^2 \times T_2^2$ and orbifold compactifications with magnetic fluxes, $M_1,M_2$, where modulus parameters are identified. This identification breaks the modular symmetry of $T^2_1 \times T^2_2$, $SL(2,\mathbb{Z})_1 \times SL(2,\mathbb{Z})_2$ to $SL(2,\mathbb{Z})\equivΓ$. Each of the wavefunctions on $T^2_1 \times T^2_2$ and orbifolds behaves as the modular forms of weight 1 for the principal congruence subgroup $Γ$($N$), $N$ being 2 times the least common multiple of $M_1$ and $M_2$. Then, zero-modes transform each other under the modular symm…
We study quark and lepton mass matrices derived from magnetized $T^2/\mathbb{Z}_2$ orbifold models. Quark and lepton masses have a large hierarchy. In addition, mixing angles are large in the lepton sector, while those are small in the quark sector. We find that this structure can be realized in certain flavor models, which are identified by the zero points of the zero-mode wave functions of fermions and Higgs modes. We classify such realistic flavor models. Fixed points $τ=i$, $e^{2πi/3}$ and $i\infty$ of the modulus $τ$ play a role in realizing a large mass hierarchy through our scenario, wh…
Massive modes on magnetized blow-up manifold of $T^2/\mathbb{Z}_N$
研究磁化吹胀流形上大规模模式的性质，通过保持磁通量和曲率不变来确保模式连续性，并发现每个奇点处局部模式数量随质量级增加而增加。
I review the basic features of four dimensional Z_2 x Z_2 (shift) orientifolds with internal magnetic fields, describing two examples with N=1 supersymmetry. As in the corresponding six-dimensional examples, D9-branes magnetized along four internal directions can mimic D5-branes, even in presence of multiplets of image branes localized on different fixed tori. Chiral low-energy spectra can be obtained if the model also contains D5-branes parallel to the magnetized directions.
We study Kähler moduli stabilizations in semi-realistic magnetized D-brane models based on $ Z_2\times Z_2'$ toroidal orbifolds. In type IIB compactifications, 3-form fluxes can stabilize the dilaton and complex structure moduli fields, but there remain some massless closed string moduli fields, Kähler moduli. The magnetic fluxes generate Fayet-Iliopoulos terms, which can fix ratios of Kähler moduli. On top of that, we consider D-brane instanton effects to stabilize them in concrete D-brane models and investigate the brane configurations to confirm that the moduli fields can be stabilized succ…
We study $T^2/Z_N$ orbifold models with magnetic fluxes. We propose a systematic way to analyze the number of zero-modes and their wavefunctions by use of modular transformation. Our results are consistent with the previous results, and our approach is more direct and analytical than the previous ones. The index theorem implies that the zero-mode number of the Dirac operator on $T^2$ is equal to the index $M$, which corresponds to the magnetic flux in a certain unit. Our results show that the zero-mode number of the Dirac operator on $T^2/Z_N$ is equal to $\lfloor M/N \rfloor +1$ except one ca…
We propose matter wavefunctions on resolutions of $T^2/\mathbb{Z}_N$ singularities with constant magnetic fluxes. In the blow-down limit, the obtained wavefunctions of chiral zero-modes result in those on the magnetized $T^2/\mathbb{Z}_N$ orbifold models, but the wavefunctions of $\mathbb{Z}_N$-invariant zero-modes receive the blow-up effects around fixed points of $T^2/\mathbb{Z}_N$ orbifolds. Such blow-up effects change the selection rules and Yukawa couplings among the chiral zero-modes as well as the modular symmetry, in contrast to those on the magnetized $T^2/\mathbb{Z}_N$ orbifold model…
Quantum aspects of non-invertible flavor symmetries in intersecting/magnetized D-brane models
本文研究环面轨道流形上IIA相交和IIB磁化D-brane模型中手性物质的选取规则，发现树级和圈级下由$D_4$味对称性描述，并探讨了D-brane瞬子等非微扰效应。
We study the CP-violating phase of the quark sector in the $U(8)$ flavor model on $T^2/Z_N \, (N=2,3,4,6)$ with non-vanishing magnetic fluxes, where properties of possible origins of the CP violation are investigated minutely. In this system, a non-vanishing value is mandatory in the real part of the complex modulus parameter $τ$ of the two-dimensional torus. On $T^2$ without orbifolding, underlying discrete flavor symmetries severely restrict the form of Yukawa couplings and it is very difficult to reproduce the observed pattern in the quark sector including the CP-violating phase $δ_{\rm CP}…
We study the flavor landscape of particle physics models based on a ten-dimensional super Yang-Mills theory compactified on magnetized tori preserving four-dimensional ${\cal N}=1$ supersymmetry. Recently, we constructed a semi-realistic model which contains the minimal supersymmetric standard model (MSSM) using an Ansatz of magnetic fluxes and orbifolding projections. However, we can consider more various configurations of magnetic fluxes and orbifolding projections preserving four-dimensional ${\cal N}=1$ supersymmetry. We research systematically such possibilities for leading to MSSM-like m…
We study the modular symmetry in $T^2$ and orbifold comfactifications with magnetic fluxes. There are $|M|$ zero-modes on $T^2$ with the magnetic flux $M$. Their wavefunctions as well as massive modes behave as modular forms of weight $1/2$ and represent the double covering group of $Γ\equiv SL(2,\mathbb{Z})$, $\widetildeΓ \equiv \widetilde{SL}(2,\mathbb{Z})$. Each wavefunction on $T^2$ with the magnetic flux $M$ transforms under $\widetildeΓ(2|M|)$, which is the normal subgroup of $\widetilde{SL}(2,\mathbb{Z})$. Then, $|M|$ zero-modes are representations of the quotient group $\widetildeΓ'_{2…
Index theorem on magnetized blow-up manifold of $T^2/\mathbb{Z}_N$
本文研究磁化 $T^2/\mathbb{Z}_N$ 轨形爆破流形上的指标定理，建立了零模计数公式并阐明其物理与几何意义。
We study non-abelian discrete flavor symmetries, which can appear in magnetized brane models. For example, $D_4$, $Δ(27)$ and $Δ(54)$ can appear and matter fields with several representations can appear. We also study the orbifold background, where non-abelian flavor symmetries are broken in a certain way.
We study T^{11-D-q}xT^q/Z_n orbifold compactifications of 11D supergravity and M-theory by a purely algebraic method. Using the mapping between scalar fields of toroidally compactified maximal supergravity and generators of the U-duality symmetry, we express the orbifold action as a finite order inner automorphism and compute the residual real U-duality algebra surviving the orbifold projection for all dimensions D=1,...,10-q. In D=1, these invariant subalgebras are shown to be described by Borcherds and Kac-Moody algebras with a degenerate Cartan matrix, modded out by their centres and deriva…
We study 10D super Yang-Mills theory with the gauge groups $E_6$, $E_7$ and $E_8$. We consider the torus/orbifold compacfitication with magnetic fluxes and Wilson lines. They lead to 4D interesting models with three families of quarks and leptons, whose profiles in extra dimensions are quasi-localized because of magnetic fluxes.
We study the modular symmetry in magnetized D-brane models on $T^2$. Non-Abelian flavor symmetry $D_4$ in the model with magnetic flux $M=2$ (in a certain unit) is a subgroup of the modular symmetry. We also study the modular symmetry in heterotic orbifold models. The $T^2/Z_4$ orbifold model has the same modular symmetry as the magnetized brane model with $M=2$, and its flavor symmetry $D_4$ is a subgroup of the modular symmetry.
We study discrete flavor symmetries of the models based on a ten-dimensional supersymmetric Yang-Mills (10D SYM) theory compactified on magnetized tori. We assume non-vanishing non-factorizable fluxes as well as the orbifold projections. These setups allow model-building with more various flavor structures. Indeed, we show that there exist various classes of non-Abelian discrete flavor symmetries. In particular, we find that $S_3$ flavor symmetries can be realized in the framework of the magnetized 10D SYM theory for the first time.
A manifestly gauge invariant formulation of 5-dimensional supersymmetric Yang-Mills theories in terms of 4d superfields is derived. It relies on a supersymmetry and gauge-covariant derivative operator in the $x^5$ direction. This formulation allows for a systematic study of higher-derivative operators by combining invariant 4d superfield expressions under the additional restriction of 5d Lorentz symmetry. In cases where the 5d theory is compactified on a gauge-symmetry-breaking orbifold, the formalism can be used for a simple discussion of possible brane operators invariant under the restricte…
We discuss the options for parity assignments in (on-shell) N=2 five-dimensional Yang-Mills-Einstein supergravity theories (YMESGTs) coupled to tensor and hypermultiplets on the orbifold spacetime M_4 X S^1/Z_2. Along the lines of orbifold-GUTs, we allow for general breaking of the five-dimensional gauge group at the orbifold fixed points. We then extend the discussion to the case where the orbifold is S^1/(Z_2xZ_2). We do not presume the existence of fields with support only at fixed points. As in the familiar case of (rigid) super-Yang-Mills theories on such orbifolds, only bulk hypermultipl…
The flavor structures on magnetized orbifold models and 4D modular symmetric models
本文研究了磁化轨形模型和4D模对称模型上的夸克与轻子味结构，发现特定零点模式可避免质量等级和混合角困难，并在无需精细微调下实现夸克质量比与CKM矩阵元素，同时构造Siegel模形式以包含CP相位。
Worldsheet techniques can be used to argue for the integrability of string theory on AdS_5xS^5/Z_S, which is dual to the strongly coupled Z_S-orbifold of N=4 SYM. We analyze the integrability of these field theories in the perturbative regime and construct the relevant Bethe equations.
We derive the partition function of {\cal N}=4 supersymmetric Yang-Mills theory on orbifold-T^4/{\bf Z}_2 for gauge group SU(N). We generalize the method of our previous work for the SU(2) case to the SU(N) case. The resulting partition function is represented as the sum of the product of Göttche formula of singular quotient space $T^4/{\bf Z}_2 $ and of blow-up formulas including A_{N-1} theta series with level N.
Non-invertible flavor symmetries in magnetized extra dimensions
本文研究磁通环面紧致化中高维杨-米尔斯理论的不可逆对称性，推导了$\mathbb{Z}_N$轨形不变的离散等距算符融合规则，证明其决定手征零模的味结构，并给出表示与选择规则。
Gravitational and gauge anomalies provide stringent constraints on which subset of chiral models can effectively describe M-theory at low energy. In this paper, we explicitly construct an abelian orbifold of M-theory to obtain an N=1, chiral super Yang-Mills theory in four dimensions, using anomaly matching to determine the entire gauge and representation structure. The model described in this paper is the simplest four dimensional model which one can construct from M-theory compactified on an abelian orbifold without freely-acting involutions. The gauge group is SO(12) x SU(8) x SU(2) x SU(2)…
We derive the partition function of N=4 supersymmetric Yang-Mills theory on orbifold-$T^4/{\bf Z}_2$. In classical geometry, K3 surface is constructed from the orbifold-$T^4/{\bf Z}_2$. Along the same way as the orbifold construction, we construct the partition function of K3 surface from orbifold-$T^4/{\bf Z}_2$. The partition function is given by the product of the contribution of the untwisted sector of $T^4/{\bf Z}_2$, and that of the twisted sector of $T^4/{\bf Z}_2$ i.e., ${\cal O}(-2)$ curve blow-up formula.
We geometrically engineer d=4 N=1 supersymmetric Yang-Mills theories by considering M theory on various Joyce orbifolds. We argue that the superpotential of these models is generated by fractional membrane instantons. The relation of this superpotential to membrane anomalies is also discussed.
We discuss the fate of the Z2 symmetry and the vacuum structure in an SU(N)xSU(N) gauge theory with one bifundamental Dirac fermion. This theory can be obtained from SU(2N) supersymmetric Yang--Mills (SYM) theory by virtue of Z2 orbifolding. We analyze dynamics of domain walls and argue that the Z2 symmetry is spontaneously broken. Since unbroken Z2 is a necessary condition for nonperturbative planar equivalence we conclude that the orbifold daughter is nonperturbatively nonequivalent to its supersymmetric parent. En route, our investigation reveals the existence of fractional domain walls, si…
We discover the unique, simple Lie Algebra of the Third Kind, or LATKe, that stems from codimension 6 orbifold singularities and gives rise to a kind of Yang-Mills theory which simultaneously is pure and contains matter. The root space of the LATKe is 1-dimensional and its Dynkin diagram consists of one point. The uniqueness of the LATKe is a vacuum selection mechanism.
We consider systems of magnetized D9 branes on orbifolds supporting N=1 gauge theories. In such realizations, the matter multiplets arise from "twisted" strings connecting different stacks of branes. The introduction of Euclidean 5-branes wrapped on the six-dimensional compact space leads to instanton effects. We examine the interplay between the annuli diagrams with an E5 boundary and the holomorphicity properties of the effective low-energy supergravity action which describes the system, including its instanton corrections. Mostly based on arXiv:0709.0245.
To explore color/kinematics duality for general representations of the gauge group we formulate the duality for general abelian orbifolds of the SU(N), N=4 super Yang-Mills theory in four dimensions, which have fields in the bi-fundamental representation, and use it to construct explicitly complete four-vector and four-scalar amplitudes at one loop. For fixed number of supercharges, graph-organized L-loop n-point integrands of all orbifold theories are given in terms of a fixed set of polynomials labeled by L representations of the orbifold group. In contrast to the standard duality-satisfying…
We revisit the problem of constructing instantons on ADE orbifolds R^4/Γand point out some subtle relations with the complex structure on the orbifold. We consider generalized instanton equations on R^4/Γwhich are BPS equations for the Yang-Mills equations with an external current. The relation between level sets of the moment maps in the hyper-Kaehler quotient construction of the instanton moduli space and sources in the Yang-Mills equations is discussed. We describe two types of spherically-symmetric Γ-equivariant connections on complex V-bundles over R^4/Γwhich are tailored to the way in wh…
We study the condensation of localized closed string tachyons on AdS orbifolds both from the bulk and boundary theory viewpoints. We first extend the known results for AdS_5/Z_k to AdS_3/Z_k case, and we proposed that the AdS_3/Z_k decays into AdS_3/Z_k' with k' < k. From the bulk viewpoint, we obtain a time-dependent gravity solution describing the decay of AdS orbifold numerically. From the dual gauge theory viewpoint, we calculated the Casimir energies of gauge theory vacua and it is found that their values are exactly the same as the masses of dual geometries, even though they are in diffe…
String Duals of Two-Dimensional Yang-Mills and Symmetric Product Orbifolds
本文提出二维大N chiral 杨-米尔斯理论与对称积奇点的弦对偶关系，并揭示了约束弦、非相对论弦与AdS$_3$/CFT$_2$之间的联系。
We study 10D super Yang-Mills E8 theory on the 6D torus compactification with magnetic fluxes. We study systematically the possibilities for realizing 4D supersymmetric standard models with three generations of quarks and leptons. We also study quark mass matrices.
We investigate the gauge coupling renormalization in orbifold field theories preserving 4-dimensional N=1 supersymmetry in the framework of 4-dimensional effective supergravity. As a concrete example, we consider the 5-dimensional Super-Yang-Mills theory on a slice of AdS_5. In our approach, one-loop gauge couplings can be determined by the loop-induced axion couplings and the tree level properties of 4-dimensional effective supergravity which are much easier to be computed.
Non-supersymmetric orbifolds of N=1 super Yang-Mills theories are conjectured to inherit properties from their supersymmetric parent. We examine this conjecture by compactifying the Z_2 orbifold theories on a spatial circle of radius R. We point out that when the orbifold theory lies in the weakly coupled vacuum of its parent, fractional instantons do give rise to the conjectured condensate of bi-fundamental fermions. Unfortunately, we show that quantum effects render this vacuum unstable through the generation of twisted operators. In the true vacuum state, no fermion condensate forms. Thus, …
All the models of elementary particles and their interactions derived from String Theory involve a compact six-dimensional internal space. Its volume and shape should be fixed or stabilized, since otherwise massless scalar fields (moduli) reflecting their deformations appear in our four-dimensional space-time, with sizable effects on known particles and fields. We propose a strategy towards stabilizing the compact space without fluxes of three-form fields from closed strings. Our main motivation and goal is to proceed insofar as possible within conventional string world-sheet theory. As we sha…
We describe discrete symmetries of two-dimensional Yang-Mills theory with gauge group $G$ associated to outer automorphisms of $G$, and their corresponding defects. We show that the gauge theory partition function with defects can be computed as a path integral over the space of twisted $G$-bundles, and calculate it exactly. We argue that its weak-coupling limit computes the symplectic volume of the moduli space of flat twisted $G$-bundles on a surface. Using the defect network approach to generalised orbifolds, we gauge the discrete symmetry and construct the corresponding orbifold theory, wh…
One-loop vacuum energy in 10D super-Yang-Mills theory on magnetized tori with/without 4D N=1 supersymmetric completion
本文利用 Barnes $ζ$ 函数计算了磁化环面上 10D 超 Yang-Mills 理论的单圈真空能，发现两种不同模型构建方式所得的真空能结果完全一致。
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