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Symmetrical laws of structure of helicoidally-like biopolymers in the framework of algebraic topology. I. Root lattice E8 and the closed sequence of algebraic polytopes [article]

M. I. Samoylovich, A. L. Talis
2012 arXiv   pre-print
These polytopes were determined by the second coordination sphere of 8-dimensional lattice E8.  ...  by the lattice E8.  ...  The algebraic polytopes and rod substructures in E 3 .Each of the 240 vectors of the first coordination sphere of the system E 8 , which determine the vertices of the eight dimensional Gosset polytope,  ... 
arXiv:1211.3686v1 fatcat:6detc4j4xvehlpppxjf6vjpope

Aspects of Symmetry, Topology and Anomalies in Quantum Matter [article]

Juven C. Wang
2016 arXiv   pre-print
In this thesis, we explore the aspects of symmetry, topology and anomalies in quantum matter with entanglement from both condensed matter and high energy theory viewpoints.  ...  The focus of our research is on the gapped many-body quantum systems including symmetry-protected topological states and topologically ordered states. Chapter 1. Introduction. Chapter 2.  ...  E8 lattices E8 , namely, 0 × = (︀ 0 1 1 0 )︀ ⊕ (︀ 0 1 1 0 )︀ ⊕ . . . . (5.54) ± × = 0 ⊕ (± E8 ) ⊕ (± E8 ) ⊕ . . .  ... 
arXiv:1602.05569v1 fatcat:kwgoiznwxbhejdewg63udo24hq

Toric Geometry and String Theory [article]

Vincent Bouchard
2006 arXiv   pre-print
on the moduli space of holomorphic maps with involution, and the topological vertex.  ...  We determine the BPS structure of the amplitudes, and illustrate our general results in various examples with and without D-branes.  ...  Any complete triangulation of the surface of ∆ * defines a fan Σ whose three dimensional cones are just the cones over the regular (i.e., lattice volume one) triangles.  ... 
arXiv:hep-th/0609123v1 fatcat:ci37n7gqyfgdhdzd565fghne2y

Landscaping with fluxes and the E8 Yukawa Point in F-theory [article]

Nana Cabo Bizet, Albrecht Klemm, Daniel Vieira Lopes
2014 arXiv   pre-print
The explicit resolution of the singularity introduce a higher dimensional fiber and leads to novel features.  ...  Integrality in the Hodge theory of Calabi-Yau fourfolds is essential to find the vacuum structure and the anomaly cancellation mechanism of four dimensional F-theory compactifications.  ...  D.V.L. was also supported by the PDJ fellowship of CNPq, grant number 501107/2012-6.  ... 
arXiv:1404.7645v1 fatcat:pnxfnu4c2jcvzbsdznmuartg44

$E_8$ gauge theory, and a derivation of $K$-theory from $M$-theory

Duiliu-Emanuel Diaconescu, Gregory Moore, Edward Witten
2002 Advances in Theoretical and Mathematical Physics  
The partition function of Ramond-Ramond p-form fields in Type IIA supergravity on a ten-manifold X contains subtle phase factors that are associated with T-duality, self-duality, and the relation of the  ...  We analyze the detailed phase factors on the two sides and show that they agree, thereby testing M-theory/Type IIA duality as well as the Jf-theory formalism in an interesting way.  ...  One simply sets where here * is the Hodge duality operator. Associated with the lattice F is a torus T = A/T where A is the vector space F ®z R.  ... 
doi:10.4310/atmp.2002.v6.n6.a2 fatcat:fiswn4nxszgsdf2i5cq7fg7jxm

E8 Gauge Theory, and a Derivation of K-Theory from M-Theory [article]

Duiliu-Emanuel Diaconescu, Gregory Moore, Edward Witten
2004 arXiv   pre-print
The analogous partition function of M-theory on X x S1 contains subtle phases that are similarly associated with E8 gauge theory.  ...  The partition function of Ramond-Ramond p-form fields in Type IIA supergravity on a ten-manifold X contains subtle phase factors that are associated with T-duality, self-duality, and the relation of the  ...  The positive or negative chirality spinors of the normal bundle are hence trivial rank eight bundles, and the number of zero modes of the Dirac operator of the world-volume fermions is divisible by eight  ... 
arXiv:hep-th/0005090v3 fatcat:7w53ahtb6rahhdik4bxfmnwka4

Origin of Abelian gauge symmetries in heterotic/F-theory duality

Mirjam Cvetič, Antonella Grassi, Denis Klevers, Maximilian Poretschkin, Peng Song
2016 Journal of High Energy Physics  
mechanism in the lower-dimensional effective theory.  ...  While the number of geometrically massless U(1)'s is determined entirely by geometry on the F-theory side, on the heterotic side the correct number of U(1)'s is found by taking into account a Stuckelberg  ...  Acknowledgments It is a pleasure to thank Hernan Piragua for initial collaboration at early stages of this project. We thank L. Anderson  ... 
doi:10.1007/jhep04(2016)041 fatcat:kb5caccbfbeuhg63cp3pqqeg4i

Many-body topological invariants for fermionic short-range entangled topological phases protected by antiunitary symmetries

Ken Shiozaki, Hassan Shapourian, Kiyonori Gomi, Shinsei Ryu
2018 Physical review B  
, and Dirac quantization conditions.  ...  We show that an important ingredient for the construction of the many-body topological invariants is a fermionic partial transpose which is basically the standard partial transpose equipped with a sign  ...  Lapa and Xueda Wen for useful discussions. This work was supported in part by the National Science Foundation grant DMR 1455296. K.S. is supported by RIKEN Special Postdoctoral Researcher Program.  ... 
doi:10.1103/physrevb.98.035151 fatcat:7sbizfb4sbbcfeoxi5kwexj5sa

SU(5) tops with multiple U(1)s in F-theory

Jan Borchmann, Christoph Mayrhofer, Eran Palti, Timo Weigand
2014 Nuclear Physics B  
We analyse the local limit of our SU(5) x U(1) x U(1) models and show that one of our models is not embeddable into E8 due to recombination of matter curves that cannot be described as a Higgsing of E8  ...  and a class of gauge fluxes.  ...  Acknowledgements We thank Sakura Schäfer-Nameki and Thomas Grimm for very interesting and useful discussions regarding the local limit of the model presented in [47] .  ... 
doi:10.1016/j.nuclphysb.2014.02.006 fatcat:svfunqhfafclhijudakwwgbmle

Chern-Simons theory on spherical Seifert manifolds, topological strings and integrable systems

Gaëtan Borot, Andrea Brini
2018 Advances in Theoretical and Mathematical Physics  
Mathematically, our results put forward an identification between the 1/N expansion of the sl N +1 LMO invariant of S Γ and a suitably restricted Gromov-Witten/Donaldson-Thomas partition function on the  ...  Guided by string theory dualities, we propose a large N dual description in terms of both A-and B-twisted topological strings on (in general non-toric) local Calabi-Yau threefolds.  ...  The work of G.B. benefits from the support of the Max-Planck Gesellschaft. The work of A.B. is partially supported by the GNFM-INdAM. 2 Chern-Simons theory and Seifert spaces  ... 
doi:10.4310/atmp.2018.v22.n2.a2 fatcat:k5g6eoim4ra4ll5lndykfanw2q

Chern-Simons theory on spherical Seifert manifolds, topological strings and integrable systems [article]

Gaetan Borot, Andrea Brini
2015 arXiv   pre-print
Mathematically, our results put forward an identification between the 1/N expansion of the sl_N + 1 LMO invariant of S^Γ and a suitably restricted Gromov-Witten/Donaldson-Thomas partition function on the  ...  Guided by string theory dualities, we propose a large N dual description in terms of both A- and B-twisted topological strings on (in general non-toric) local Calabi-Yau threefolds.  ...  P 1 yields a pure gauge field theory in d = 4 with eight supercharges and no hypermultiplets as the effective four-dimensional theory.  ... 
arXiv:1506.06887v2 fatcat:a2nh72ekm5d6lfnfuoeq7ir2oi

A slow review of the AGT correspondence [article]

Bruno Le Floch
2022 arXiv   pre-print
This 6d construction yields the Coulomb branch and Seiberg-Witten geometry of class S theories, geometrizes S-duality, and leads to the AGT correspondence, which states that many observables of class S  ...  This is an extended writeup of the lectures given at the Winter School YRISW 2020, to appear in a special issue of JPhysA.  ...  Acknowledgments First, many thanks to Jaume Gomis for guiding me through basics of the AGT correspondence starting a decade ago, and to my other coauthors on AGT-related papers for  ... 
arXiv:2006.14025v3 fatcat:6aaptyl5vvhirdzitvcriz67ze

5d SCFTs from decoupling and gluing

Fabio Apruzzi, Sakura Schäfer-Nameki, Yi-Nan Wang
2020 Journal of High Energy Physics  
Finally, inspired by the quiver structure of 6d theories, we propose a gluing construction for 5d SCFTs from building blocks and their CFDs.  ...  In the M-theory realization the latter case corresponds to decompactification of a set of compact surfaces in the Calabi-Yau threefold.  ...  This work is supported by the ERC Consolidator Grant number 682608 "Higgs bundles: Supersymmetric Gauge Theories and Geometry (HIGGSBNDL)". plot the configuration of curves in figure 13 .  ... 
doi:10.1007/jhep08(2020)153 fatcat:fyv637bacbaybfk5hivw4x3xla

5d SCFTs from Decoupling and Gluing [article]

Fabio Apruzzi, Sakura Schafer-Nameki, Yi-Nan Wang
2020 arXiv   pre-print
Finally, inspired by the quiver structure of 6d theories, we propose a gluing construction for 5d SCFTs from building blocks and their CFDs.  ...  In the M-theory realization the latter case corresponds to decompactification of a set of compact surfaces in the Calabi-Yau threefold.  ...  Rudelius, and G. Zafrir for discussions. This work is supported by the ERC Consolidator Grant number 682608 "Higgs bundles: Supersymmetric Gauge Theories and Geometry (HIGGSBNDL)".  ... 
arXiv:1912.04264v4 fatcat:uke4t7mbqzdpjh6ucwoo5wvkni

Axion Dark Matter Research with IBS/CAPP [article]

Yannis K. Semertzidis, Jihn E. Kim, SungWoo Youn, Jihoon Choi, Woohyun Chung, Selcuk Haciomeroglu, Dongmin Kim, Jingeun Kim, ByeongRok Ko, Ohjoon Kwon, Andrei Matlashov, Lino Miceli (+25 others)
2019 arXiv   pre-print
In this report, the current status and future prospects of the experiments and R&D activities at IBS/CAPP are described.  ...  The axion, a consequence of the PQ mechanism, has been considered as the most elegant solution to the strong-CP problem and a compelling candidate for cold dark matter.  ...  The reason that the "invisible" axion from U(1) anom has N DW = 1 is because N from E8×E 8 = large integer but N MI axion = 1 [57, 42], and N from E8×E 8 and N MI axion are relatively prime.  ... 
arXiv:1910.11591v1 fatcat:idrtyj7cmvfnrgoitswja5ncf4
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