Differential models for the Anderson dual to bordism theories and invertible QFT's

[APS75a]

M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry. II, Math. Proc. Cambridge Philos. Soc. 78 (1975) 405–432.

[APS75b]

, Spectral asymmetry and Riemannian geometry. I, Math. Proc. Cambridge Philos. Soc. 77 (1975) 43–69.

[APS76]

, Spectral asymmetry and Riemannian geometry. III, Math. Proc. Cambridge Philos. Soc. 79 (1976) 71–99.

[BS10]

U. Bunke and T. Schick, Uniqueness of smooth extensions of generalized cohomology theories, J. Topol. 3 (2010) 110–156.

[BS12]

, Differential K-theory: a survey, Global differential geometry,

Springer Proc. Math., vol. 17, Springer, Heidelberg, 2012, pp. 303–357.

https://doi.org/10.1007/978-3-642-22842-1_11.

[BSSW09] U. Bunke, T. Schick, I. Schr¨

oder, and M. Wiethaup, Landweber exact formal

group laws and smooth cohomology theories, Algebr. Geom. Topol. 9 (2009)

1751–1790.

[BT06]

M. Brightwell and P. Turner, Relative differential characters, Comm. Anal.

Geom. 14 (2006) 269–282.

[Bun12]

U. Bunke, Differential cohomology, 2013. arXiv:1208.3961 [math.AT].

[CFLS19a] C. C´

ordova, D. S. Freed, H. T. Lam, and N. Seiberg, Anomalies in the Space

of Coupling Constants and Their Dynamical Applications I, SciPost Phys. 8

(2020) 001, arXiv:1905.09315 [hep-th].

, Anomalies in the Space of Coupling Constants and Their Dynamical

[CFLS19b]

Applications II, SciPost Phys. 8 (2020) 002, arXiv:1905.13361 [hep-th].

[CL20]

C.-M. Chang and Y.-H. Lin, On Exotic Consistent Anomalies in (1+1)d: A

Ghost Story, arXiv:2009.07273 [hep-th].

[CS85]

J. Cheeger and J. Simons, Differential characters and geometric invariants,

Geometry and topology (College Park, Md., 1983/84), Lecture Notes in

Math., vol. 1167, Springer, Berlin, 1985, pp. 50–80. https://doi.org/10.

1007/BFb0075216.

[DL20]

J. Davighi and N. Lohitsiri, The algebra of anomaly interplay, SciPost Phys.

10 (2021) 074, arXiv:2011.10102 [hep-th].

[FH21]

D. S. Freed and M. J. Hopkins, Reflection positivity and invertible topological

phases, Geom. Topol. 25 (2021) 1165–1330.

[FL10]

D. S. Freed and J. Lott, An index theorem in differential K-theory, Geom.

Topol. 14 (2010) 903–966.

[FMS07]

D. S. Freed, G. W. Moore, and G. Segal, The uncertainty of fluxes, Comm.

Math. Phys. 271 (2007) 247–274.

[Fre95]

D. S. Freed, Classical Chern-Simons theory. I, Adv. Math. 113 (1995) 237–

303.

, Classical Chern-Simons theory. II, vol. 28, 2002, pp. 293–310. Special

[Fre02]

issue for S. S. Chern.

[Fre14]

, Anomalies and Invertible Field Theories, Proc. Symp. Pure Math.

88 (2014) 25–46, arXiv:1404.7224 [hep-th].

[Fre19]

, Lectures on field theory and topology, CBMS Regional Conference

Series in Mathematics, vol. 133, American Mathematical Society, Providence,

RI, 2019. https://doi.org/10.1090/cbms/133. Published for the Conference

Board of the Mathematical Sciences.

[GS21]

D. Grady and H. Sati, Differential KO-theory: constructions, computations,

and applications, Adv. Math. 384 (2021) Paper No. 107671, 117.

80

[HKT20]

P.-S. Hsin, A. Kapustin, and R. Thorngren, Berry Phase in Quantum Field

Theory: Diabolical Points and Boundary Phenomena, Phys. Rev. B 102

(2020) 245113, arXiv:2004.10758 [cond-mat.str-el].

[HS05]

M. J. Hopkins and I. M. Singer, Quadratic functions in geometry, topology,

and M-theory, J. Differential Geom. 70 (2005) 329–452.

[HTY19]

C.-T. Hsieh, Y. Tachikawa, and K. Yonekura, Anomaly of the Electromagnetic Duality of Maxwell Theory, Phys. Rev. Lett. 123 (2019) 161601,

arXiv:1905.08943 [hep-th].

[HTY20]

, Anomaly inflow and p-form gauge theories, arXiv:2003.11550

[hep-th].

[J¨

an68]

K. J¨

anich, On the classification of O(n)-manifolds, Math. Ann. 176 (1968)

53–76.

[Joy12]

D. Joyce, On manifolds with corners, Advances in geometric analysis, Adv.

Lect. Math. (ALM), vol. 21, Int. Press, Somerville, MA, 2012, pp. 225–258.

[Kap14]

A. Kapustin, Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology, arXiv:1403.1467 [cond-mat.str-el].

[Klo08]

K. R. Klonoff, An index theorem in differential K-theory, ProQuest LLC, Ann Arbor, MI, 2008. http://gateway.proquest.com/

openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:

dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3321109. Thesis

(Ph.D.)–The University of Texas at Austin.

[KS21]

M. Kontsevich and G. Segal, Wick Rotation and the Positivity of Energy

in Quantum Field Theory, Quart. J. Math. Oxford Ser. 72 (2021) 673–699,

arXiv:2105.10161 [hep-th].

[KTTW14] A. Kapustin, R. Thorngren, A. Turzillo, and Z. Wang, Fermionic Symmetry Protected Topological Phases and Cobordisms, JHEP 12 (2015) 052,

arXiv:1406.7329 [cond-mat.str-el].

[LMSN18] C. Lawrie, D. Martelli, and S. Sch¨

afer-Nameki, Theories of Class F and Anomalies, JHEP 10 (2018) 090, arXiv:1806.06066 [hep-th].

[LOT20]

Y. Lee, K. Ohmori, and Y. Tachikawa, Revisiting Wess-Zumino-Witten terms,

SciPost Phys. 10 (2021) 061, arXiv:2009.00033 [hep-th].

[MN84]

G. W. Moore and P. C. Nelson, Anomalies in Nonlinear σ Models, Phys. Rev.

Lett. 53 (1984) 1519.

[MN85]

, The Etiology of σ Model Anomalies, Commun. Math. Phys. 100

(1985) 83.

[Mon19]

S. Monnier, A Modern Point of View on Anomalies, Fortsch. Phys. 67 (2019)

1910012, arXiv:1903.02828 [hep-th].

[NR61]

M. S. Narasimhan and S. Ramanan, Existence of universal connections, Amer.

J. Math. 83 (1961) 563–572.

[Rud98]

Y. B. Rudyak, On Thom spectra, orientability, and cobordism, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 1998. With a foreword by

Haynes Miller.

[ST19]

A. Schwimmer and S. Theisen, Osborn Equation and Irrelevant Operators, J.

Stat. Mech. 1908 (2019) 084011, arXiv:1902.04473 [hep-th].

[STY18]

N. Seiberg, Y. Tachikawa, and K. Yonekura, Anomalies of Duality

Groups and Extended Conformal Manifolds, PTEP 2018 (2018) 073B04,

arXiv:1803.07366 [hep-th].

[Tho17]

R. Thorngren, Topological Terms and Phases of Sigma Models,

arXiv:1710.02545 [cond-mat.str-el].

[TY17]

Y. Tachikawa and K. Yonekura, Anomalies involving the space of couplings

and the Zamolodchikov metric, JHEP 12 (2017) 140, arXiv:1710.03934

[hep-th].

[TY21]

Y. Tachikawa and M. Yamashita, Topological modular forms and the absence

of all heterotic global anomalies, 2021. arXiv:2108.13542 [hep-th].

[Upm15]

M. Upmeier, Algebraic structure and integration maps in cocycle models for

differential cohomology, Algebr. Geom. Topol. 15 (2015) 65–83.

81

[Wit83]

[WY19]

[WZ71]

[Yam21]

[Yon18]

[YY21]

E. Witten, Global Aspects of Current Algebra, Nucl. Phys. B 223 (1983) 422–

432.

E. Witten and K. Yonekura, Anomaly Inflow and the η-Invariant, The

Shoucheng Zhang Memorial Workshop, 9 2019. arXiv:1909.08775 [hep-th].

J. Wess and B. Zumino, Consequences of anomalous Ward identities, Phys.

Lett. B 37 (1971) 95–97.

M. Yamashita, Differential models for the Anderson dual to bordism theories

and invertible QFT’s, II, 2021. arXiv:2110.14828 [math.AT].

K. Yonekura, On the cobordism classification of symmetry protected topological phases, Commun. Math. Phys. 368 (2019) 1121–1173, arXiv:1803.10796

[hep-th].

M. Yamashita and K. Yonekura, Differential models for the Anderson dual to

bordism theories and invertible QFT’s, I, arXiv:2106.09270 [math.AT].

...