اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAn Analysis of Anomaly Cancellation for Theories in D=10
75
0
0.0
(
0
)
تأليف
Andrea Antonelli
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We prove that the swampland for D=10 N=1 SUGRA coupled to D=10 N=1 SYM is only populated by U(1)^496 and E_8 x U(1)^248. With this goal in mind, we review the anomalies for classical and exceptional groups, retrieving trace identities up to the sixth power of the curvature for each class of groups. We expand this idea for low-dimensional groups, for which the trace of the sixth power is known to factorize, and we retrieve such factorization. We obtain the total anomaly polynomials for individual low dimensional groups and combinations of them and finally we investigate their non-factorization, in such a way that U(1)^496and E_8 xU(1)^248 are non-trivially shown to be the only anomaly-free theories allowed in D=10. Using the method developed for checking the factorization of gauge theories, we retrieve the Green-Schwarz terms for the two theories populating the swampland.
قيم البحث
اقرأ أيضاً
Many extensions of the Standard Model include an extra gauge boson, whose couplings to fermions are constrained by the requirement that anomalies cancel. We find a general solution to the resulting diophantine equations in the plausible case where th
e chiral fermion content is that of the Standard Model plus 3 right-handed neutrinos.
We present calculation of the anomaly cancellation in M-theory on orbifolds $S^1/Z_2$ and $T^5/Z_2$ in the upstairs approach. The main requirement that allows one to uniquely define solutions to the modified Bianchi identities in this case is that th
e field strength $G$ be globally defined on $S^1$ or $T^5$ and properly transforming under $Z_2$. We solve for general $G$ that satisfies these requirements and explicitly construct anomaly-free theories in the upstairs approach. We also obtain the solutions in the presence of five-branes. All these constructions show equivalence of the downstairs and upstairs approaches. For example in the $S^1/Z_2$ case the ten-dimensional gauge coupling and the anomaly cancellation at each wall are the same as in the downstairs approach.
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-q
uantized in the generalized cohomology theory called J-twisted Cohomotopy.
In this note we review the role of homotopy groups in determining non-perturbative (henceforth `global) gauge anomalies, in light of recent progress understanding global anomalies using bordism. We explain why non-vanishing of $pi_d(G)$ is neither a
necessary nor a sufficient condition for there being a possible global anomaly in a $d$-dimensional chiral gauge theory with gauge group $G$. To showcase the failure of sufficiency, we revisit `global anomalies that have been previously studied in 6d gauge theories with $G=SU(2)$, $SU(3)$, or $G_2$. Even though $pi_6(G) eq 0$, the bordism groups $Omega_7^mathrm{Spin}(BG)$ vanish in all three cases, implying there are no global anomalies. In the case of $G=SU(2)$ we carefully scrutinize the role of homotopy, and explain why any 7-dimensional mapping torus must be trivial from the bordism perspective. In all these 6d examples, the conditions previously thought to be necessary for global anomaly cancellation are in fact necessary conditions for the local anomalies to vanish.
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 Ho
rava-Wittens 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.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
