Home page of

Gregory W. Moore

 

Directory information

  Position:

Faculty

  Research group:

High Energy Theory

  Email address:

gmoore@physics.rutgers.edu

  Telephone:

(732) 445-4375

  Dept. Fax:

(732) 445-4343

  Office:

Serin E362

  Mailing address:

Greg Moore
NHETC
Department of Physics and Astronomy
Rutgers, The State University of New Jersey
136 Frelinghuysen Road
Piscataway, NJ 08854-8019 USA

Teaching

Information for Physics 695, Fall 2013.

Applied Group Theory, Physics 618, Spring 2013.

Advanced Topics in Mathematical Physics, Fall 2010. will be offered instead. Lectures can be viewed online here

Research Activities

My work focuses on mathematical physics, with an emphasis on string theory, M-theory, and gauge theories more generally.
My work places particular emphasis on the underlying mathematical structures and applications to and from modern mathematics.
Specific research interests include:

  1. The theory of branes and generalized abelian gauge theories in supergravity.
    This involves interesting topological issues related to generalized differential cohomology theories, especially K-theory.
    There are also interesting relations to the theory of self-dual fields, anomaly cancellation, and noncommutative geometry.
  2. Effective low energy supergravity theories in string compactification and the computation of nonperturbative stringy effects in effective supergravities.
  3. D-branes on Calabi-Yau manifolds and BPS state counting. Relations to Borcherds products, automorphic forms, black-hole entropy, and wall-crossing.
  4. Applications of the theory of automorphic forms to conformal field theory, string compactification, black hole entropy counting, and the AdS/CFT correspondence.
  5. Potential connections to number theory. For example - I pointed out in 1998 that the attractor mechanism
    of supersymmetric black holes singles out Calabi-Yau varieties with relations to complex multiplication.
  6. Conformal field theories. Rational conformal field theories, especially applications to the theory of anyons and nonabelions.
  7. Topological field theories, and applications to invariants of manifolds.
  8. String field theory.
  9. String cosmology and time-dependence in string theory
  10. Does the alleged ``landscape of N=1 effective four-dimensional string vacua'' really exist?

 

Expository, Historical, and Philosophical

 

  1. ``What is a brane?'' . Published in: Notices of the American Mathematical Society, Vol. 52, No. 2, pp.214-215.
  2. ``How many black holes fit on the head of a pin?'', coauthored with Frederik Denef. Published in: Int.J.Mod.Phys. D17 (2008) 679-684, Gen.Rel.Grav. 39 (2007) 1539-1544 .
  3. ``The Impact of D-branes on Mathematics''. I wrote this trying to collect my thoughts before appearing on a panel at JOEFEST at the KITP, February 2014 .
  4. ``Response to the 2014 Eisenbud Prize''. I wrote this since the AMS requested a response.
  5. ``Some Comments on Physical Mathematics''. I wrote this to try to collect my thoughts, preparing a talk for the 2014 Heineman Prize. It is an expansion on the previous essay. The talk is here .
  6. ``Physical Mathematics and the Future''. This is the essay which is meant to accompany my ``vision talk'' in the summary section of Strings 2014 in Princeton.

 

Publications

(Almost all publications after August 1991 are available on the e-print arXiv .)

 

  1. Anomalous Inequivalence of Phenomenological Theories, (with A. Manohar),  Nucl. Phys. {\bf B243}(1984)55.
  2. Anomalies and Odd Dimensions, (with L. Alvarez-Gaum\'e
    and S. Della Pietra) Ann. Phys. (1985)288
  3. Anomalies in Nonlinear Sigma Models, (with P. Nelson),
    Phys. Rev. Lett. {\bf 53}(1984)1519
  4. Constraints on a Two-Higgs Interpretation of the
    $\zeta(8.3)$, (with H. Georgi and A. Manohar), Phys. Lett.
    {\bf 149B}(1984)234
  5. The Aeteology of Sigma Model Anomalies, (with P. Nelson)
    Comm. Math. Phys. {\bf 100}(1985)83
  6. A Comment on Sigma Model Anomalies, (with A. Manohar and
    P. Nelson) Phys. Lett. {\bf 152B}(1985)68
  7. Measure for Moduli, (with P. Nelson), Nucl. Phys.
    {\bf B266}(1986)58
  8. An Off-Shell Propagator for String Theory, (with
    A. Cohen, P. Nelson, and J. Polchinski), Nucl. Phys.
    {\bf B267}(1986)143
  9. An Invariant String Propagator (with A. Cohen, P. Nelson,
    and J. Polchinski) in {\it Unified String Theories}, D. Gross and
    M. Green eds., World Scientific (1986)
  10. Strings and supermoduli (with P.~Nelson, and J.~Polchinski)
     Phys.~Lett. {\bf B169} (1986) 47; {\bf201B} (1988) 579(E)
  11. Heterotic geometry, (with P. Nelson), Nucl. Phys.
    {\bf B274} (1986) 509
  12. An $O(16)\times O(16)$ Heterotic String, (with L. Alvarez-Gaum\'e,
    P. Ginsparg, and C. Vafa) Phys. Lett. {\bf 171B}(1986)155
  13. Theta Functions, Modular Invariance, and Strings,
    (with L. Alvarez-Gaum\'e, and C. Vafa), Comm. Math. Phys.
    {\bf 106}(1986)1
  14. Semi-Off-Shell String Amplitudes (with A. Cohen,
    P. Nelson, and J. Polchinski), Nucl. Phys. {\bf B281}(1986)127
  15. Modular forms and Two-Loop String Physics, Phys. Lett.
    {\bf 176B}(1986)369
  16. Bosonization in Arbitrary Genus, (with L. Alvarez-Gaum\'e,
    J. B. Bost, P. Nelson, and C. Vafa) Phys. Lett. {\bf 178B}(1986)41
  17. Bosonization on higher genus Riemann surfaces,
    (with L.~Alvarez-Gaum\'e, J.~B.~Bost, P. Nelson, and C.~Vafa),
    Commun. Math. Phys. {\bf112} (1987) 503
  18. Modular forms and the cosmological constant,
    (with J. Harris, P. Nelson, and I. Singer)
    Phys.\ Lett.\ {\bf178B} (1986) 167; {\bf201B} (1988) 579(E)
  19. Modular Forms and Multiloop String Physics, in
    {\it Proceedings of the VIIIth International Congress on
    Mathematical Physics} at Marseille.
    M. Mebkhout, ed. World Scientific, 1987, pp. 776-783
  20. Atkin-Lehner Symmetry, Nucl. Phys. {\bf B293}(1987)139
  21. Vanishing Vacuum Energies for Nonsupersymmetric Strings,
    in {\it Nonperturbative Quantum Field Theory} (Cargese lectures),
    G. Mack,
    G. `t Hooft, A. Jaffe, P. Mitter, and R. Stora, eds.
    Plenum.
  22. Quasicrystalline Compactification, (with J. Harvey and
    C. Vafa) Nucl. Phys. {\bf B304}(1988)269
  23. Some Remarks on Two-Loop Superstring Calculations,
    (with A. Morozov), Nucl. Phys. {\bf B306}(1988)387
  24. Some global issues in string
    perturbation theory,
    " (with J. J. Atick, and A. Sen),
    Nucl. Phys. B308(1988)1-101
  25. Rationality in Conformal Field Theory, (with
    G. Anderson), Comm. Math. Phys. {\bf 117}(1988)441
  26. Catoptric tadpoles, (with J. J. Atick, and A. Sen)
    Nucl. Phys. B307(1988)221
  27. Strings in the Operator Formalism, (with L. Alvarez-Gaum\'e,
    C. Gomez, and C. Vafa), Nucl. Phys. {\bf 303}(1988)455
  28. Polynomial Equations for Rational Conformal Field
    Theories, (with N. Seiberg),
    Phys. Lett.  {\bf 212B}(1988)451
  29. Naturality in Conformal Field Theory,
    (with N. Seiberg), Nucl. Phys. {\bf B313}(1989)16
  30. Classical and Quantum Conformal Field Theory,
    (with N. Seiberg), Commun. Math. Phys. {\bf 123}(1989)177
  31. Taming the Conformal Zoo,
    (with N. Seiberg), Phys. Lett. {\bf 220B}(1989)422
  32. A Comment on Quantum Group Symmetry in Conformal Field
    Theory, (with N. Reshetikhin), Nucl. Phys. {\bf B328}(1989)557
  33. Remarks on the Canonical Quantization of the Chern-Simons-
    Witten Theory, (with S. Elitzur, A. Schwimmer, and N. Seiberg),
    Nucl. Phys. {\bf B326}(1989)108
  34. Rational Conformal Field Theory and Group Theory,
    (with N. Seiberg), in the proceedings of the
    Schloss Ringberg conference, April 1989
  35. Lectures on Rational Conformal Field Theory,
    (with N. Seiberg), in {\it Strings '89},Proceedings
    of the Trieste Spring School on Superstrings,
    3-14 April 1989, M. Green, et. al. Eds. World
    Scientific, 1990.
  36. The Ising model, the Yang-Lee edge singularity, and
    2D quantum gravity, (with \v C. Crnkovi\'c and P. Ginsparg),
    Phys. Lett. {\bf 237B}(1990)196
  37. Nonabelions in the fractional quantum hall effect, (with N. Read),
    Nucl. Phys. 360B(1991)362
  38. Geometry of the String Equations, Commun. Math. Physics.
    {\bf 133}(1990) 261-304
  39. Physical Solutions for Unitary-Matrix Models
    (with M. Douglas and C. Crnkovic), Nucl. Phys. {\bf B360}(1991)507
  40. Simplex Equations and Their Solutions, (with I. Frenkel),
    Commun. Math. Phys. {\bf 138}(1991)259
  41. Matrix Models of 2D Gravity and Isomonodromic Deformation,
    in Common Trends in Mathematics and Quantum Field
    Theories, T. Eguchi et. al., eds. Prog. Theor. Phys. Suppl.
    102; Also, in the  Proceedings of the
    1990 Carg\'ese Workshop on Random Surfaces, Quantum Gravity and
    Strings, with slightly improved version.
  42. Multicritical Multi-Cut Matrix Models, (with \v C. Crnkovi\'c),
    Phys. Lett. {\bf B257}(1991)322
  43. Double-Scaled Field Theory at c=1, Nucl.Phys.B368:557-590,1992,
  44. Boundary Operators in 2D Gravity, (with E. Martinec and
    N. Seiberg), Phys. Lett.   B263 (1991)190.
  45. From Loops to States in 2D Quantum Gravity, (with N. Seiberg
    and M. Staudacher), Nucl. Phys.   B362 (1991)665
  46. Loop Equations and the Topological Phase of Multi-Cut Matrix
    Models, (with \v C. Crnkovi\'c and M. Douglas),  hep-th/9108014;
    Int.J.Mod.Phys.A7:7693-7711,1992
  47. From Loops to Fields in 2D Quantum Gravity (with N. Seiberg),
    Int. Jour. Mod. Phys. {\bf 7A}(1992)2601.
  48. Exact S-Matrix for 2D String Theory, (with R. Plesser and S.
    Ramgoolam),
    hepth/9111035; Nucl.Phys.B377:143-190,1992
  49. Gravitational Phase Transitions and the Sine-Gordon Model
  50. Classical Scattering in 1+1 Dimensional String Theory, (with R.
    Plesser), hepth/9203060; Phys.Rev.D46:1730-1736,1992
  51. Fractional quantum Hall effect and nonabelian statistics, (with
    N. Read),  hepth/9111035;
    to appear in Proceedings of 4th Yukawa International Symposium
  52. The partition function of 2d string theory, (with R. Dijkgraaf and
    R. Plesser),  hepth/9208031; Nucl.Phys.B394:356-382,1993
  53. Lectures on 2D Gravity and 2D String Theory, (with P. Ginsparg),
     hepth/9304011; in {\it Recent Directions in Particle Theory}, J. Harvey
    and J. Polchinski,
    eds., World Scientific, 1993
  54. Finite in All Directions, hepth/9305139
  55. Symmetries and Symmetry-Breaking in String Theory,
     hepth/9308052; in {\it International Workshop on
    Supersymmetry and Unification of Fundamental
    Forces}, P. Nath, ed, World Scientific 1993
  56. Symmetries of the bosonic string $S$-matrix,
     hep-th/9310026
  57. Large N 2D Yang-Mills Theory and Topological String Theory,
     http://arxiv.org/abs/hep-th/9402107. Commun.Math.Phys.185:543-619,1997
  58. Chaotic Coupling Constants, (with J. Horne)
      Nucl.Phys.B432:109-126,1994
  59. Addendum to: ``Symmetries of the Bosonic String S-Matrix,
     http://arxiv.org/abs/hep-th/9404025. Nucl.Phys.B432:109-126,1994



Some Recent Talks

 

  1. Lectures at the Les Houches Meeting on Number Theory, Geometry, and
    Physics. Les Houches, March 9-21, 2003.
  2. Localized tachyon flows and Hirzebruch-Jung spaces, at the conference
    ``Avant Strings,'' Institut des Hautes Etudes Scientifiques, Paris, June 15, 2004.
  3. On the quantization of Page charges, at the conference
    ``Avant Strings,'' Institut des Hautes  Etudes Scientifiques, Paris, June 23, 2004
  4. Anomalies, Gauss Laws, and Page charges, at the conference
    ``Strings 2004,'' Paris, July 1, 2004.
  5. Testing some Black Hole/Topological String conjectures,  Institute
    for Advanced Study, April 11, 2005
  6. Lie Algebras, BPS States, and String Duality, Summer workshop on
    Groups and Algebras in M-theory
    , Rutgers Math Department, May 31, 2005
  7. Black holes and Arithmetic, Talk delivered at the Mathematicshe Arbeitstagung,
    Max Planck Institute, Bonn, Germany, 11 June 2005.
  8. Remarks on the Hamiltonian Formulation of Some
    Generalized Abelian Gauge Theories, Talk delivered at the workshop,
     Geometric Topology and Connections with
    Quantum Field Theory,
    Oberwolfach, Germany, June 13, 2005.
  9. Noncommutativity of Electric and Magnetic Fluxes, Amsterdam Workshop on
    String Theory,
      June 22, 2005,
  10. Electric and Magnetic Flux Do Not Commute, Aspen Workshop in Superstring
    Cosmology
    , Aspen, Co, August 9, 2005
  11. Mathematics Aspects of Fluxes,, KITP Workshop on Mathematics of String Theory,
    Cosmology
    , Santa Barbara, October 11, 2005
  12. An uncertainty principle for fluxes, with applications to self-dual fields, , CUNY, June 28, 2006 (26th International Colloquium on Group Theoretical Methods in Physics)
  13. Split Polar Attractors , Harvard, September 29, 2006
  14. Wall-crossing and an entropy enigma , Strings 2007, Madrid, June 28,2007. For question period see this link.
  15. An Uncertainty Principle for Topological Sectors , Jurg Frohlich birthday Celebration, Zurich, July 2, 2007
  16. Wall-crossing formulae for BPS states and some applications , Clay Mathematics Institute workshop on K3's and modular forms,
    Cambridge, Mass, March 20, 2008
  17. Four lectures on modular forms and black hole entropy , Trieste Spring School on Superstrings, Trieste, March 25-April 4, 2008.
  18. Mathematical Foundations of Orientifolds , UCSB, July 18, 2008
  19. Four-dimensional wall-crossing from three-dimensional field theory , KITP Miniprogram on Langlands Duality, July 31, 2008.
  20. Wall-crossing formulae for BPS states and some applications , Zurich Prestrings, Zurich, August 11, 2008
  21. Four-dimensional wall-crossing from three-dimensional field theory , Zurich Prestrings, Zurich, August 12, 2008
  22. Mathematical Foundations of Orientifolds , Zurich Prestrings, Zurich, August 11, 2008
  23. Update on Wall-Crossing , Strings 2008, CERN, August 22, 2008. Video of the talk available here.
  24. Improved version of the Prestrings/KITP talk, Four-dimensional wall-crossing from three-dimensional field theory, 3rd New England String Meeting, Brown University, Oct. 24, 2008
  25. Extremal N=2, 2D CFT and Constraints of Modularity Institute for Advanced Study, Nov. 5, 2008
  26. Overview of the theory of Self-dual fields AMS Meeting, Washington DC, Jan. 8, 2009. A pdf version is available here
  27. Four-dimensional wall-crossing from three-dimensional field theory Simons Center Workshop, StonyBrook, Jan. 13, 2009
  28. Orientifolds, Twisted Cohomology, and Self-Duality A talk at the Conference on Perspectives in Mathematics and Physics in honor of I.M. Singer's 85th birhday, MIT, May 23, 2009. For further material see the talk by Dan Freed and the talk by Jacques Distler
  29. BPS States, Hitchin Systems, and the WKB Approximation Workshop on Mirror Symmetry, Hausdorff Center for Mathematics, Bonn, June 3, 2009
  30. Here is a minicourse (half of which) was given at the Galileo Galilei Institute and at Frascati, in June 2009. Lecture 1 covers basics of the BPS wall-crossing phenomenon. Lecture 2 reviews the work with D. Gaiotto and A. Neitzke on the relation of the KSWCF to hyperkahler geometry. Lecture 3 and Lecture 4 review the paper on the relation to Hitchin Systems and the WKB approximation.
  31. The RR charge of an orientifold, Michigan Conference on Topology and Physics, Ann Arbor, Feb. 7, 2010 and Oberwolfach workshop, June 8,2010
  32. Say ``halo!'' to new walls and new indices, Strings2010, Texas A& M, March 15, 2010. Video of the talk in Monday, Session 3 is available here
  33. Line Operators in N=2 Gauge Theories, Simons Center Workshop on Quantum Teichmuller Theory, SUNY, Stonybrook, March 30, 2010. The paper is available here
  34. PiTP Lectures on Wall-Crossing, PiTP School at the Institute for Advanced Study, July 27-29, 2010. These are pedagogical notes on Wall-Crossing in four-dimensional N=2 theories. Video available here .
  35. Minicourse of three lectures on Generalized Abelian Gauge Theories, Self-Duality, and Differential Cohomology, at the Simons Center Workshop on Differential Cohomology, Simons Center for Geometry and Physics, Stonybrook, Jan. 11-14, 2011. Here are Lecture Notes . Video available here .
  36. Surface defects in d=4, N=2 theories, BPS states, wall-crossing, and hyperkahler geometry, Simons Center Workshop on Branes and Bethe Ansatz, SCGP, March 25, 2011 Here are Lecture Notes . Video available here .
  37. Modular Tensor Categories from Six Dimensional Field Theories, Symposium For Michael Freedman's 60th Birthday, KITP, UCSB, April 16, 2011. Video available here .
  38. Surface defects and the BPS spectrum of 4d N=2 theories, IHES, Three Strings Generations, Paris, May 17, 2011. Powerpoint presentation here . A slightly different version presented at the Solvay Conference in Brussels is here .
  39. On Recent Applications of Six Dimensional (0,2) Theory to Physical Mathematics, Review Talk at Strings 2011, Uppsala, Sweden, June 29, 2011 Powerpoint presentation here . A pdf version is here . Video available here .
  40. Three Transverse Intersections Between Physical Mathematics and Condensed Matter Theory, at the Conference Strongly Interacting Electrons in Low Dimensions: New Orders, Symmetries, and Excitations, in honor of Duncan Haldane's 60th birthday. Princeton, September 14, 2011. Powerpoint presentation here .
  41. A very long lecture on the physical relation of Donaldson to Seiberg-Witten invariants of four-manifolds. A 4.5 hour-long lecture, with 40pp. of texed handouts presented at the Simons Center for Geometry and Physics School on Supersymmetric Field Theories and Their Implications, March 8, 2012. Video and lecture notes available here .
  42. Spectral Networks and Their Applications, Caltech, March 30, at the conference ``N=4 Super Yang-Mills Theory, 35 years after.'' Powerpoint presentation here .
  43. Progress in D=4, N=2 Field Theory, Strings-Math 2012, Bonn, July 2012 Powerpoint presentation here .
  44. Lectures at St. Ottilien: Quantum Symmetries and K-Theory. Lecture notes here .
  45. Plenary talk at the ICMP in Aalborg, Denmark, August 8, 2012. Powerpoint version here and pdf here .
  46. Felix Klein Lectures: ``Applications of the six-dimensional (2,0) theory to physical mathematics.'' October 1 - 11, 2012 at the Hausdorff Insitute for Mathematics, Bonn. Lecture notes, which are still very much UNDER CONSTRUCTION, are available here . Constructive comments, criticisms and reference requests are welcome. You could watch the videos of the actual lectures here . However, I am reminded of Mark Twain's wonderful chapter conclusion: ``Let us draw the curtain of charity over the rest of the scene.''
  47. The talk I would have given at the Simons Center for Geometry and Physics on Oct. 31, if hurricane Sandy hadn't gotten in the way, is here . It is called ``BPS Degeneracies and Hyperkahler Geometry.''
  48. A report on work in progress with D. Gaiotto and E. Witten, given at the conference "Aspects of Topology" for G. Segal's 70th birthday is here . A pdf version is here .
  49. Here is the talk I gave at the SCGP workshop ``Topological Phases of Matter.'' A pdf version is here . Video of the talk is here .
  50. Here is the talk I gave at the Strings 2013 conference in Seoul, South Korea. A pdf version is here . Video of the talk is here .
  51. An update on the work in progress with D. Gaiotto and E. Witten, "Algebra of the Infrared,'' given at the SCGP conference "Quiver Varieties," Oct. 15, 2013 is here . A pdf version is here . This talk is directed more at mathematicians than physicists.
  52. A version of the previous talk, "Algebra of the Infrared: Massive d=2 N=(2,2) QFT'', or ``A short ride with a big machine,'' given at the KITP Workshop on Nonperturbative Methods in Field Theory, March 11, 2014 is here . A pdf version is here . This talk is directed more at physicists than mathematicians. (The actual talk at the KITP was an unmitigated disaster due to technical problems with the projector. The video is not recommended.)
  53. This version emphasizes the formal webology apparatus, "Web formalism and the IR limit of d=2 N=(2,2) QFT'', or ``A short ride with a big machine,'' scheduled to be given at String-Math2014, June 12, 2014: here . A pdf version is here . This talk is directed more at mathematicians than physicists.

 

·       Clay Mathematical Institute Lectures

 

If you are looking for  ``D-branes and K-theory in 2D topological field theory,’’ hep-th/0609042  you can get a pdf file here Dbranes_Ktheory_Final.pdf,

Or a postscript file here (warning 23MB!) Dbranes_Ktheory_Final.ps, or you can get   the tex file Dbranes_Ktheory_Final.tex, and the  figures as    ClayFigsFinal_EPS.zip   or  as  ClayFigsFinal_GIF.zip


Please send any comments on this page to gmoore@physics.rutgers.edu.

Revised May 20, 2007