K-Theory from a physical perspective

This is an expository paper which aims at explaining a physical point of view on the K-theoretic classification of D-branes. We combine ideas of renormalization group flows between boundary conformal field theories, together with spacetime notions such as anomaly cancellation and D-brane instanton effects. We illustrate this point of view by describing the twisted K-theory of the special unitary groups SU(N).

[1]  J. Maldacena,et al.  Geometrical interpretation of D-branes in gauged WZW models , 2001, hep-th/0105038.

[2]  An illustrated guide to D-branes in SU(3) , 2001, hep-th/0111221.

[3]  K. Hori.  Linear Models of Supersymmetric D-Branes , 2000, hep-th/0012179.

[4]  K-Theory in Quantum Field Theory , 2002, math-ph/0206031.

[5]  Stefan Fredenhagen,et al.  Branes on group manifolds, gluon condensates, and twisted K-theory , 2001 .

[6]  J. Mickelsson.  Gerbes, (twisted) K-theory, and the supersymmetric WZW model , 2002, hep-th/0206139.

[7]  Stringy Higgs mechanism and the fate of open strings , 2000, hep-th/0011009.

[8]  A Derivation of K theory from M theory , 2000, hep-th/0005090.

[9]  Superconnections, anomalies and non-BPS brane charges , 2001, hep-th/0108043.

[10]  Boundaries, defects and Frobenius algebras , 2003, hep-th/0302200.

[11]  Integrable Structure of Conformal Field Theory III. The Yang–Baxter Relation , 1998, hep-th/9805008.

[12]  J. Cardy,et al.  Bulk and boundary operators in conformal field theory , 1991 .

[13]  D-Branes And K-Theory , 1998, hep-th/9810188.

[14]  E. Witten.  Supersymmetry and Morse theory , 1982 .

[15]  Tension is dimension , 1999, hep-th/9909072.

[16]  D. Lewellen.  Sewing constraints for conformal field theories on surfaces with boundaries , 1992 .

[17]  D-branes, Matrix Theory and K-homology , 2001, hep-th/0108085.

[18]  S. Donaldson.  Geometry of four-manifolds , 1990 .

[19]  A. Jaffe,et al.  Quantum K-theory. II. Homotopy invariance of the Chern character☆ , 1990 .

[20]  Daniel S. Freed.  Dirac Charge Quantization and Generalized Differential Cohomology , 2000 .

[21]  A. Alekseev,et al.  RR charges of D2-branes in the WZW model , 2000, hep-th/0007096.

[22]  V. Schomerus.  Lectures on Branes in Curved Backgrounds , 2002, hep-th/0209241.

[23]  C. Schweigert,et al.  The geometry of WZW branes , 1999, hep-th/9909030.

[24]  K. algebras.  String duality, automorphic forms, and generalized Kac-Moody algebras , 1997 .

[25]  Michael J. Hopkins,et al.  Twisted equivariant K‐theory with complex coefficients , 2002, math/0206257.

[26]  A. Ludwig,et al.  Universal noninteger "ground-state degeneracy" in critical quantum systems. , 1991, Physical review letters.

[27]  A. Jaffe,et al.  Index of a family of Dirac operators on loop space , 1987 .

[28]  A unified framework for the Kondo problem and for an impurity in a Luttinger liquid , 1995, cond-mat/9510055.

[29]  Integrable structure of conformal field theory, quantum KdV theory and Thermodynamic Bethe Ansatz , 1994, hep-th/9412229.

[30]  Constructing D-branes from K theory , 1999, hep-th/9907140.

[31]  J. Pawełczyk.  SU(2) WZW D-branes and their noncommutative geometry from DBI action , 2000, hep-th/0003057.

[32]  Nathan Seiberg,et al.  D-Brane Instantons and K-Theory Charges , 2001 .

[33]  D. Freed,et al.  Anomalies in string theory with D-branes , 1999, hep-th/9907189.

[34]  On the relevance of tachyons , 2000, hep-th/0003101.

[35]  Witten.  On background-independent open-string field theory. , 1992, Physical review. D, Particles and fields.

[36]  D-brane charges in five-brane backgrounds , 2001, hep-th/0108152.

[37]  Homotopy field theory in dimension 2 and group-algebras , 1999, math/9910010.

[38]  V. Snaith.  On the Kunneth formula spectral sequence in equivariant K- theory , 1972, Mathematical Proceedings of the Cambridge Philosophical Society.

[39]  E. Witten.  Baryons and branes in anti de Sitter space , 1998, hep-th/9805112.

[40]  C. Lazaroiu.  On the structure of open-closed topological field theory in two-dimensions , 2000, hep-th/0010269.

[41]  Noncommutative tachyons and K-theory , 2000, hep-th/0009030.

[42]  A. Ludwig,et al.  Exact conformal-field-theory results on the multichannel Kondo effect: Single-fermion Green's function, self-energy, and resistivity. , 1993, Physical review. B, Condensed matter.

[43]  M. Mariño.  On the BV formulation of boundary superstring field theory , 2001, hep-th/0103089.

[44]  M. Douglas,et al.  D-Branes on Calabi-Yau Manifolds , 2000, math/0009209.

[45]  E. Witten.  Overview of K theory applied to strings , 2000, hep-th/0007175.

[46]  Conformal boundary states for free bosons and fermions , 2001, hep-th/0108238.

[47]  Some computations in background-independent off-shell string theory. , 1992, Physical review. D, Particles and fields.

[48]  Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation , 1996, hep-th/9604044.

[49]  WZW BRANES AND GERBES , 2002, hep-th/0205233.

[50]  Nathan Seiberg,et al.  String theory and noncommutative geometry , 1999 .

[51]  K-theory and Ramond-Ramond charge , 1997, hep-th/9710230.

[52]  Remarks on Tachyon Condensation in Superstring Field Theory , 2000, hep-th/0010108.

[53]  On Decay of K-theory , 2002, hep-th/0212059.

[54]  C. Schweigert,et al.  Conformal Field Theory, Boundary Conditions and Applications to String Theory , 2000, hep-th/0011109.

[55]  C. Schweigert,et al.  Category theory for conformal boundary conditions , 2001, math/0106050.

[56]  P. Bouwknegt,et al.  D branes on group manifolds and fusion rings , 2002 .

[57]  Boundary string field theory of the D anti-D system , 2000, hep-th/0012198.

[58]  Flux stabilization of D-branes , 2000, hep-th/0003037.

[59]  Twisted K-Theory and K-Theory of Bundle Gerbes , 2001, hep-th/0106194.

[60]  Organizing boundary RG flows , 2003, hep-th/0301229.

[61]  L. Hodgkin.  The equivariant Künneth theorem in K-theorem , 1975 .

[62]  Daniel S. Freed,et al.  The Verlinde algebra is twisted equivariant K-theory , 2001, math/0101038.

[63]  D-branes, B fields and twisted K theory , 2000, hep-th/0002023.

[64]  M. Douglas,et al.  Two lectures on D-geometry and noncommutative geometry , 1999, hep-th/9901146.

[65]  D. Freed,et al.  Twisted K-theory and loop group representations , 2003, math/0312155.

[66]  A. Jaffe,et al.  QuantumK-theory , 1988 .

[67]  Map of Witten's ★ to Moyal's ★ , 2001, hep-th/0106157.

[68]  Boundary Wzw,et al.  Institute for Mathematical Physics , 2022 .

[69]  K-theory and S-duality: starting over from square 3 , 2001, hep-th/0112084.

[70]  E. Witten.  GLOBAL ANOMALIES IN STRING THEORY , 1985 .

[71]  Some exact results on tachyon condensation in string field theory , 2000, hep-th/0009148.

[72]  A. Tseytlin.  Born-Infeld action, supersymmetry and string theory , 1999, hep-th/9908105.

[73]  Alain Connes,et al.  Renormalization in quantum field theory and the Riemann-Hilbert problem , 1999 .

[74]  D-Branes And Mirror Symmetry , 2000, hep-th/0005247.

[75]  On the Algebras of BPS States , 1996, hep-th/9609017.

[76]  A. Sen.  Tachyon condensation on the brane antibrane system , 1998, hep-th/9805170.

[77]  Alain Connes,et al.  Renormalization in Quantum Field Theory and the Riemann–Hilbert Problem I: The Hopf Algebra Structure of Graphs and the Main Theorem , 2000 .

[78]  Defects, Decay, And Dissipated States , 2002, hep-th/0210231.

[79]  W. Lerche,et al.  Boundary rings and /N=2 coset models , 2000 .