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| Matrix string theory | |
|---|---|
| Name | Matrix string theory |
| Field | Theoretical physics |
| Contributors | Tom Banks, Wati Taylor, Nathan Seiberg, Leonard Susskind, Tomás Ortín, Michael R. Douglas, Edward Witten, Andrew Strominger, Cumrun Vafa, Juan Maldacena, Joseph Polchinski, Ashoke Sen, Paul Townsend, Hugh Osborn, Chris Hull, Barton Zwiebach, Erik Verlinde, Herman Verlinde, Nicolas Nekrasov, Nima Arkani-Hamed, Gary Gibbons, Shamit Kachru, Richard Myers, Matt Strassler |
| Introduced | 1997 |
| Institutions | Institute for Advanced Study, Harvard University, Princeton University, California Institute of Technology, Stanford University, Rutgers University, University of Cambridge, University of California, Berkeley |
Matrix string theory is a nonperturbative framework proposing that two-dimensional supersymmetric gauge theories encode the dynamics of perturbative strings and capture aspects of eleven-dimensional M-theory in particular limits. It relates matrix models, derived from discrete light-cone quantization and D-brane dynamics, to perturbative string spectra and interactions, providing a bridge between Type IIA string theory, M-theory, and gauge theory descriptions. The approach influenced developments in AdS/CFT correspondence, dualities in string theory, and noncommutative geometry.
Matrix string theory emerged from attempts to understand nonperturbative aspects of Type IIA string theory using matrix models inspired by the BFSS matrix model and the Matrix theory conjecture. Key figures in the formulation included researchers associated with Rutgers University, Harvard University, and University of California, Santa Barbara. The formalism builds on concepts from D0-brane quantum mechanics, light-front quantization, and supersymmetric Yang–Mills theory in two dimensions, making contact with established results from Perturbative string theory and results from the Seiberg–Witten theory era.
Motivation traces to attempts to formulate a nonperturbative definition of M-theory after breakthroughs at Strings '95 and influential lectures at ICTP. The BFSS proposal, stemming from work by Tom Banks, Wati Taylor, Leonard Susskind, and others, suggested that large N matrices of D0-branes reproduce eleven-dimensional physics in the infinite momentum frame studied by Paul Townsend and Edward Witten. Subsequent efforts by Nati Seiberg, Lubos Motl, and teams at Princeton University adapted these ideas to string interactions and second-quantized string descriptions, with influential seminars at IAS shaping the development. Connections to earlier work on matrix models of two-dimensional gravity and the c=1 matrix model provided technical precedents.
The basic formulation uses a two-dimensional U(N) supersymmetric gauge theory with (8,8) supersymmetry arising from dimensional reduction of N=1 supersymmetric Yang–Mills theory in ten dimensions, connected to stacks of D1-branes and D0-branes via T-duality and S-duality transformations studied by Ashoke Sen and Joseph Polchinski. The action incorporates matrix-valued fields corresponding to transverse coordinates, fermions transforming under SO(8), and a Yang–Mills coupling related to the string coupling through relationships found by Michael Douglas and Gregory Moore. Quantization employs light-cone gauge techniques refined in work by Sergio Ferrara and others, while instanton and monopole configurations echo studies by Gerard 't Hooft and Alexander Polyakov.
Matrix string theory explicitly realizes aspects of M-theory compactified on a circle via identification with discrete light-cone quantization and the DLCQ approach developed in discussions at Strings '97 workshops. Duality webs involving T-duality, S-duality, and U-duality connect the matrix gauge theory to Type IIB string theory, heterotic string theory, and F-theory constructions explored by Cumrun Vafa and Gavin Salam. Relations to the AdS/CFT correspondence proposed by Juan Maldacena highlight how matrix descriptions mirror gauge/gravity dualities investigated at MIT and Caltech research groups. Nonperturbative ingredients like M2-brane and M5-brane physics were probed using techniques pioneered by Paul Townsend and Andrew Strominger.
Compactification on circles, orbifolds, and tori employs techniques from studies at CERN and DESY on moduli stabilization and flux backgrounds, invoking Kaluza–Klein theory analogies and Calabi–Yau manifolds used in Strominger–Yau–Zaslow mirror symmetry. Backgrounds with Ramond–Ramond flux and NSNS fields connect to D-brane worldvolume actions treated in work by Clifford Johnson and Barton Zwiebach, while nontrivial holonomies and Wilson lines mirror analyses by Edward Witten in heterotic compactifications. Applications to orbifold conformal field theories draw on constructions by Kurt Hori and Cumrun Vafa.
In the weak coupling and large N limits, the matrix gauge theory reproduces perturbative string spectra including massless supergravity modes first cataloged by Michael Green and John Schwarz and massive string excitations studied by David Gross. Scattering amplitudes and string interactions emerge from matrix model instantons and join–split processes similar to earlier light-cone string field theory methods developed by Masanori Sato and Lubos Motl. Comparative analyses with results from Conformal Field Theory approaches at Princeton and vertex operator methods by Alexander Belavin and Al. Zamolodchikov validate aspects of the perturbative spectrum.
Matrix string theory has been applied to questions about black hole microstates investigated by Strominger and Andy Strominger, noncommutative gauge theories analyzed by Nathan Seiberg and M.R. Douglas, and aspects of cosmological singularities studied by groups at University of Cambridge and Stanford University. Open problems include rigorous derivations of finite N corrections emphasized in workshops at Perimeter Institute, understanding interactions beyond leading order probed in collaborations at KITP, and fully incorporating M5-brane dynamics as discussed by Edward Witten and Juan Maldacena. Further connections to modern developments such as topological string theory, quantum information, and applications to condensed matter physics remain active research frontiers tackled by teams at Harvard, Caltech, and MIT.