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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]

2012
*
arXiv
*
pre-print

These polytopes were determined by

arXiv:1211.3686v1
fatcat:6detc4j4xvehlpppxjf6vjpope
*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, ...##
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Aspects of Symmetry, Topology and Anomalies in Quantum Matter
[article]

2016
*
arXiv
*
pre-print

In this thesis, we explore

arXiv:1602.05569v1
fatcat:kwgoiznwxbhejdewg63udo24hq
*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*) ⊕ . . . ...##
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Toric Geometry and String Theory
[article]

2006
*
arXiv
*
pre-print

on

arXiv:hep-th/0609123v1
fatcat:ci37n7gqyfgdhdzd565fghne2y
*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. ...##
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Landscaping with fluxes and the E8 Yukawa Point in F-theory
[article]

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. ...

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

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. ...

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

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*...

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

2016
*
Journal of High Energy Physics
*

mechanism in

doi:10.1007/jhep04(2016)041
fatcat:kb5caccbfbeuhg63cp3pqqeg4i
*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 ...##
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Many-body topological invariants for fermionic short-range entangled topological phases protected by antiunitary symmetries

2018
*
Physical review B
*

,

doi:10.1103/physrevb.98.035151
fatcat:7sbizfb4sbbcfeoxi5kwexj5sa
*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. ...##
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SU(5) tops with multiple U(1)s in F-theory

2014
*
Nuclear Physics B
*

We analyse

doi:10.1016/j.nuclphysb.2014.02.006
fatcat:svfunqhfafclhijudakwwgbmle
*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] . ...##
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Chern-Simons theory on spherical Seifert manifolds, topological strings and integrable systems

2018
*
Advances in Theoretical and Mathematical Physics
*

Mathematically, our results put forward an identification between

doi:10.4310/atmp.2018.v22.n2.a2
fatcat:k5g6eoim4ra4ll5lndykfanw2q
*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 ...##
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Chern-Simons theory on spherical Seifert manifolds, topological strings and integrable systems
[article]

2015
*
arXiv
*
pre-print

Mathematically, our results put forward an identification between

arXiv:1506.06887v2
fatcat:a2nh72ekm5d6lfnfuoeq7ir2oi
*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. ...##
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A slow review of the AGT correspondence
[article]

2022
*
arXiv
*
pre-print

This 6d construction yields

arXiv:2006.14025v3
fatcat:6aaptyl5vvhirdzitvcriz67ze
*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 ...##
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5d SCFTs from decoupling and gluing

2020
*
Journal of High Energy Physics
*

Finally, inspired by

doi:10.1007/jhep08(2020)153
fatcat:fyv637bacbaybfk5hivw4x3xla
*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 . ...##
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5d SCFTs from Decoupling and Gluing
[article]

2020
*
arXiv
*
pre-print

Finally, inspired by

arXiv:1912.04264v4
fatcat:uke4t7mbqzdpjh6ucwoo5wvkni
*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)". ...##
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Axion Dark Matter Research with IBS/CAPP
[article]

2019
*
arXiv
*
pre-print

In this report,

arXiv:1910.11591v1
fatcat:idrtyj7cmvfnrgoitswja5ncf4
*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. ...
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