Hisham Sati, Urs Schreiber
We highlight what seems to be a remaining subtlety in the argument for the cancellation of the total anomaly associated with the M5-brane in M-theory. Then we prove that this subtlety is resolved under the hypothesis that the C-field flux is charge-quantized in the generalized cohomology theory called J-twisted Cohomotopy.
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We show that charge-quantization of the M-theory C-field in J-twisted Cohomotopy implies emergence of a higher Sp(1)-gauge field on single heterotic M5-branes, which exhibits worldvolume twisted String structure.
We consider the hypothesis that the C-field 4-flux and 7-flux forms in M-theory are in the image of the non-abelian Chern character map from the non-abelian generalized cohomology theory called J-twisted Cohomotopy theory. We prove for M2-brane backgrounds in M-theory on 8-manifolds that such charge quantization of the C-field in Cohomotopy theory implies a list of expected anomaly cancellation conditions, including: shifted C-field flux quantization and C-field tadpole cancellation, but also the DMW anomaly cancellation and the C-field's integral equation of motion.
There are fundamental open problems in the precise global nature of RR-field tadpole cancellation conditions in string theory. Moreover, the non-perturbative lift as M5/MO5-anomaly cancellation in M-theory had been based on indirect plausibility arguments,lacking a microscopic underpinning in M-brane charge quantization. We provide a framework for answering these questions, crucial not only for mathematical consistency but also for phenomenological accuracy of string theory, by formulating the M-theory C-field on flat M-orientifolds in the generalized cohomology theory called Equivariant Cohom…
We characterize the integral cohomology and the rational homotopy type of the maximal Borel-equivariantization of the combined Hopf/twistor fibration, and find that subtle relations satisfied by the cohomology generators are just those that govern Horava-Witten's proposal for the extension of the Green-Schwarz mechanism from heterotic string theory to heterotic M-theory. We discuss how this squares with the Hypothesis H that the elusive mathematical foundation of M-theory is based on charge quantization in J-twisted Cohomotopy theory.
The full 6d Hopf-Wess-Zumino term in the action functional for the M5-brane is anomalous as traditionally defined. What has been missing is a condition implying the higher analogue of level quantization familiar from the 2d Wess-Zumino term. We prove that the anomaly cancellation condition is implied by the hypothesis that the C-field is charge-quantized in twisted Cohomotopy theory. The proof follows by a twisted/parametrized generalization of the Hopf invariant, after identifying the full 6d Hopf-Wess-Zumino term with a twisted homotopy Whitehead integral formula, which we establish.
We combine rational homotopy theory and higher Lie theory to describe the WZW term in the M5-brane sigma model. We observe that this term admits a natural interpretation as a twisted 7-cocycle on super-Minkowski spacetime with coefficients in the rational 4-sphere. This exhibits the WZW term as an element in twisted cohomology, with the twist given by the cocycle of the M2-brane. We consider integration of this rational situation to differential cohomology and differential cohomotopy.
Gauge potentials on the M5 brane in twisted equivariant cohomotopy
本文探讨了M5膜上规范势的全局完成问题，通过扭曲等变上同调理论推导出传统公式，并验证了其与Bianchi恒等式的一致性。
The Character Map in Twisted Equivariant Nonabelian Cohomology
本文提出了在扭曲等变非阿贝尔上同调理论中构造 Chern 特征映射类似物的一般方法，并以扭曲等变上同伦为示例，展望了其在推导 M5 膜上任意子量子态的应用。
In this paper, we construct for higher twists that arise from cohomotopy classes, the Chern character in higher twisted K-theory, that maps into higher twisted cohomology. We show that it gives rise to an isomorphism between higher twisted K-theory and higher twisted cohomology over the reals. Finally we compute spherical T-duality in higher twisted K-theory and higher twisted cohomology in very general cases.
M5 brane to D4 brane via cyclification of rational relative 3-cohomotopy
本文通过有理相对3上同调的循环化，推导了D4膜世界面上流的Bianchi恒等式，并推测出非阿贝尔相对上同调理论。
It has been proposed that gauge and Kaehler anomalies in four-dimensional type IIB orientifolds are cancelled by a generalized Green-Schwarz mechanism involving exchange of twisted RR-fields. We explain how this can be understood using the well-known duality between linear and chiral multiplets. We find that all the twisted fields associated to the N=1 sectors and some of the fields associated to the N=2 sectors reside in linear multiplets. But there are no linear multiplets associated to order-two twists. Only the linear multiplets contribute to anomaly cancellation. This suffices to cancel a…
A systematic program is developed for analyzing and cancelling local anomalies on networks of intersecting orbifold planes in the context of M-theory. Through a delicate balance of factors, it is discovered that local anomaly matching on the lower-dimensional intersection of two orbifold planes may require twisted matter on those planes which do not conventionally support an anomaly (such as odd-dimensional planes). In this way, gravitational anomalies can, in principle, tell us about (twisted) gauge groups on subspaces which are not necessarily ten-, six- or two-dimensional. An example is wor…
M(atrix) theory on an orbifold and classical two-branes therein are studied with particular emphasis to heterotic M(atrix) theory on $S_1/Z_2$ relevant to strongly coupled heterotic and dual Type IA string theories. By analyzing orbifold condition on Chan-Paton factors, we show that three choice of gauge group are possible for heterotic M(atrix) theory: SO(2N), SO(2N+1) or USp(2N). By examining area-preserving diffeomorphism that underlies the M(atrix) theory, we find that each choices of gauge group restricts possible topologies of two-branes. The result suggests that only the choice of SO(2N…
We derive and generalize the RR twisted tadpole cancellation conditions necessary to obtain consistent D=4, Z_N orbifold compactifications of Type IIB string theory. At least two different types of branes (or antibranes with opposite RR charges) are introduced into the construction. The matter spectra and their contribution to the non-abelian gauge anomalies are computed. Their relation with the tadpole cancellation conditions is also reviewed. The presence of tachyons is a common feature for some of the non-supersymmetric systems of branes.
We study non-BPS D-branes in the type II string vacua with chiral space-time SUSY constructed based on the asymmetric orbifolds of $\mbox{K3} \cong T^4/{\Bbb Z}_2$ as a succeeding work of arXiv:1704.05262[hep-th]. We especially focus on the fractional D-branes that contains the contributions from the twisted sector of the ${\Bbb Z}_2$ orbifolding. We show that the cylinder partition functions for these fractional branes do not vanish, as in the cases of ordinary non-BPS D-branes. This aspect is in a sharp contrast with the bulk-type branes studied in arXiv:1704.05262[hep-th]. We then discuss t…
In this paper we consider orbifold compactifications of M-theory on $S^1/{\bf Z}_2\times T^4/{\bf Z}_2$. We discuss solutions of the local anomaly matching conditions by twisted vector, tensor and hypermultiplets confined on the local orbifold six-planes. In addition we consider phase-transitions among different solutions which are mediated by M-theory fivebranes which touch the local orbifold planes and are converted there to gauge instantons.
Based on the twisted R-R tadpole cancellation conditions at the singularities of D=4 Type IIB orbifold $T^6/ Z_3$, we propose a new bottom-up approach to embed standard model with three generations into string theory.
We consider six-dimensional supergravity compactified on orbifolds with Wilson lines and bulk flux. Torus Wilson lines are decomposed into Wilson lines around the orbifold fixed points, and twisted boundary conditions of matter fields are related to fractional localized flux. Both, orbifold singularities and flux lead to chiral fermions in four dimensions. We show that in addition to the standard bulk and fixed point anomalies the Green-Schwarz term also cancels the four-dimensional anomaly induced by the flux background. The two axions contained in the antisymmetric tensor field both contribu…
Holomorphic supergravity in ten dimensions and anomaly cancellation
本文提出一种十维全纯超引力理论，通过量子化二次涨落并消除奇异性，揭示其与$SU(5)$扭曲超引力及I型Kodaira-Spencer理论的关系。
We discuss the construction of six- and four-dimensional Type IIB orientifolds with vanishing untwisted RR tadpoles, but generically non-zero twisted RR tadpoles. Tadpole cancellation requires the introduction of D-brane systems with zero untwisted RR charge, but non-zero twisted RR charges. We construct explicit models containing branes and antibranes at fixed points of the internal space, or non-BPS branes partially wrapped on it. The models are non-supersymmetric, but are absolutely stable against decay to supersymmetric vacua. For particular values of the compactification radii tachyonic m…
In string theory D-branes can be classified by the RR-charge they carry. In the simplest case the quantized RR-charge takes values in K-theory of the spacetime manifold. However, if the D-brane worldvolume is not spin^c or if there is a background B-field present, the Freed-Witten anomaly cancellation condition requires the RR-charge to take values in twisted K-theory. Twisted K-theory can be defined using the language of noncommutative geometry, thus opening up a possibility for noncommutative generalizations, in particular of the Minasian-Moore formula for the classical approximation of the …
The possibility of radiative gauge symmetry breaking on D3-branes at non-supersymmetric orbifold singularities is examined. As an example, a simple model of D3-branes at non-supersymmetric C^3/Z_6 singularity with some D7-branes for the cancellations of R-R tadpoles in twisted sectors is analyzed in detail. We find that there are no tachyon modes in twisted sectors, and NS-NS tadpoles in twisted sectors are canceled out, though uncanceled tadpoles and tachyon modes exist in untwisted sectors. This means that this singularity background is a stable solution of string theory at tree level, thoug…
Intersecting Dp-branes often give rise to chiral fermions living on their intersections. We study the construction of four-dimensional chiral gauge theories by considering configurations of type II D(3+n)-branes wrapped on non-trivial n-cycles on T^{2n} x(R^{2(3-n)}/Z_N), for n=1,2,3. The gauge theories on the four non-compact dimensions of the brane world-volume are generically chiral and non-supersymmetric. We analyze consistency conditions (RR tadpole cancellation) for these models, and their relation to four-dimensional anomaly cancellation. Cancellation of U(1) gauge anomalies involves a …
A symmetry-twisted boundary condition of the path integral provides a suitable framework for the semi-classical analysis of nonperturbative quantum field theories (QFTs), and we reinterpret it from the viewpoint of the Hilbert space. An appropriate twist with the unbroken symmetry can potentially produce huge cancellations among excited states in the state-sum, without affecting the ground states; we call this effect "quantum distillation". Quantum distillation can provide the underlying mechanism for adiabatic continuity, by preventing a phase transition under $S^1$ compactification. We revis…
D-branes and orientifolds on quasicrystalline orbifold backgrounds
本研究构造了六维IIB型准晶轨道流形的定向流形后裔，通过计算振幅和消除蝌蚪得到满足反常约束的真空，并构建了Brane超对称破缺及五维定向流形，证明准晶背景可支持受控开弦完备化。
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