Thursday, 13-Oct-2016 12:22:51 EDT

RESUMÉ: Warren Siegel

RESEARCH: High-energy theoretical physics

"MAJOR" PUBLICATIONS (see also "The Free Library" below):

  1. Simplifying algebra in Feynman graphs, part II: Spinor helicity from the spacecone, hep-ph/9801220, Phys.Rev.D59(1999)045013 (with G. Chalmers) --- new, easiest way to do QCD graphs; derives & simplifies "spinor helicity"
  2. Superspace duality in low-energy superstrings, hep-th/9305073, Phys.Rev.D48(1993)2826 --- invention of so-called "double field theory"
  3. Gauge string fields from the light cone, Nucl.Phys.B282(1987)125 (with B. Zwiebach) --- free gauge-invariant actions for any theory in any dimension
  4. Covariantly second-quantized string II, Phys.Lett.149B(1984)157, 151B(1985)391 --- invention of (covariant) string field theory
  5. Manifest Lorentz invariance sometimes requires nonlinearity, Nucl.Phys.B238(1984)307 --- chiral bosons
  6. Hidden local supersymmetry in the supersymmetric particle action, Phys.Lett.128B(1983)397 --- "kappa" symmetry
  7. Supergraphity (II). Manifestly covariant rules and higher loop finiteness, Nucl.Phys.B201(1982)292 (with M.T. Grisaru) --- power counting for extended supersymmetry (later used for finiteness proof for N=4)
  8. Improved methods for supergraphs, Nucl.Phys.B159(1979)429, (with M.T. Grisaru and M. Roček)
  9. Unextended superfields in extended supersymmetry, Nucl.Phys.B156(1979)135 --- Chern-Simons terms in actions
  10. Supersymmetric dimensional regularization via dimensional reduction, Phys.Lett.84B(1979)193


My main interest is confinement. It's the least understood ingredient of the Standard Model. It's the key to understanding the strong interactions. It might even be the key to understanding quantum gravity.

Confinement is a long-distance effect ("infrared slavery"). The leading infrared behavior of Quantum ChromoDynamics (or any theory containing massless Yang-Mills) is the same as that of N=4 supersymmetric Yang-Mills. The S-matrices in this theory are simpler than those of any other theory based on Yang-Mills, including the Standard Model.

My goals are:

  1. to find better ways to calculate field theory S-matrices (including the incorporation of Yangian symmetry), and
  2. to find string formulations of Yang-Mills theories that produce S-matrices resembling those for hadrons in the real world (and thus understand confinement).
Some useful interrelated methods are:
  1. Projective superspace is a subspace of the full superspace (like chiral superspace, but real) that is the only successful method for describing 4D N=2 supersymmetric theories in a manifestly supersymmetric (& conformally supersymmetric) way. Some of my research (mostly with Jain) involves generalizing these results to be more useful @ the quantum level (as Grisaru, Roček, & I did for N=1); & to N=3, which is effectively the same as N=4.
  2. The AdS/CFT correspondence allows strings to bring light on 4D quantum field theory, and vice versa. I'm focusing in particular on S-matrices, corresponding to closed strings with worldsheet boundaries coinciding with the boundary of anti-de Sitter space, corresponding to evaluating correlation functions of gauge singlets (each a loop of the boundary) or S-matrices of fundamental fields (all forming a single loop, as a single color trace).
  3. The spacecone gauge explains and gives a simpler form of the "spinor helicity" rules that make S-matrix calculations in Yang-Mills tractable (work with Chalmers). It has an especially interesting interpretation on AdS₅×S⁵: After Wick rotating the sphere to resemble AdS, the spacelike bulk coordinates of each can be combined to form the complex, null coordinates that define spacecone quantization. The surviving superspace coordinates are then just these 2 coordinates and those of 4D N=4 projective superspace.
  4. T-theory (sometimes called "double field theory" when restricted to massless fields) is an approach to manifesting the "T-duality" symmetry of string theory. It has recently been applied (with Poláček) to AdS/CFT to formulate the 10D Type IIB supergravity fields of AdS, & the complete set of 4D N=4 Yang-Mills BPS operators to which they couple, in terms of a single field living on projective superspace.
  5. F-theory is a proposed generalization of string theory, T-theory, & M-theory. It has only recently (with W. Linch) been given a concrete formulation as a theory of dynamical, fundamental membranes (& their higher-dimensional generalizations). This formulation manifests not only T-duality symmetry, but also S- & U-duality, icnluding the symmetry of eceptional groups found in maximally symmetric supergravity in various dimensions.
  6. A modification of the boundary conditions of T-theory (with O. Hohm, Zwiebach, Huang, E. Yuan, & M. Leite), or of ordinary string theory, yields a chiral string that reproduces the simplified all-dimension amplitudes of Cachazo, He, & Yuan.


Selfduality & conformal invariance

I found that all free conformal theories contain only selfdual or anti-selfdual states. I showed that a string thought to be inconsistent in positive dimensions ("N=4") was actually a more symmetric formulation of a consistent string theory ("N=2") known to describe selfdual theories. Chalmers and I showed that selfdual theories can be used as the lowest order in a perturbative helicity expansion in theories such as QCD, and developed spacecone gauge quantization to explain, systematize, and further simplify spinor helicity methods in QCD.

Particle 1st-quantization

First-quantization has been the most useful calculational tool in string theory; similar advantages have not yet been realized for particles. Dai & I analyzed 1st-quantization for scalar theories. Dai, Y. Huang, & I generalized this to 4D Yang-Mills.


With Nastase, Roiban, and Hatsuda I studied a new version of the correspondence between 4D conformal field theory and string theory on anti-de Sitter backgrounds, initiated by Maldacena. Based on the random lattice worldsheet, Dirac's projective lightcone, supertwistors, and a double holography for both anti deSitter space and the 5-sphere, we found a relation in projective superspace to the conformal field theory describing the constituents of strings (partons/preons), as distinguished from the usual one describing open string states themselves (e.g., "gluons" instead of massless "rho mesons" in hadronic string language). Dai, R.-N. Huang, & I found the explicit propagator for the supergravity field strengths on the AdS₅×S⁵ background.

More strings

I showed how so-called T-duality, rather than being a symmetry of certain string solutions, can actually be considered a spontaneously broken symmetry of the full (super)string theory. I showed that the apparent phenomenon of closed strings appearing as bound states of open strings actually occurs as a kinematic effect in the free theory, analogously to a similar phenomenon in field theory in two dimensions ("bosonization"). Feng and I showed how to use gauge covariant vertex operators in string theory that automatically give S-matrices with gauge independent external line factors. Lee and I solved the long-standing problem of finding the BRST operator for the manifestly supersymmetric superstring, and used this formalism to give simpler calculations of tree & 1-loop superstring amplitudes.

Strings on random lattices

I extended to superstrings the random matrix approach to string theory, in which the string appears as a bound state of particles, and early results (with Feng) suggest that the superstring arises as a bound state of a type of supersymmetric quantum chromodynamics. Biswas, Grisaru, and I calculated explicit ladder diagrams in random lattice theory to derive linear Regge trajectrories.

Extra dimensions

Biswas and I studied the various ways extra internal dimensions could be used to describe N=2 supersymmetric theories, and evaluate their actions. We also found a new type of dimensional reduction, radial instead of linear, which gives theories in (anti) de Sitter space from flat space.


Lee and I showed how to reproduce supergravity at one loop as a bound state of super Yang-Mills using higher-derivative couplings, a result previously thought unique to string theory. The mechanism is similar to the UV/IR correspondence found in noncommutative field theory, but is Lorentz covariant. Like string theory, this phenomenon uniquely requires D=10 and supersymmetry. Hatsuda and I generalized to superspace results of Snyder on compact momentum space, which has the same form of Lorentz covariant noncommutativity, describing supersymmetric theories on a Lorentz covariant "lattice".

Short distance modifications to spacetime

I showed that the gravity implied by string theory weakens at short distances, as was suggested by its preonic substructure found in random lattice quantization, and implies the absence of black holes. Biswas, Mazumdar, & I generalized this to cosmology, showing the absence of a singularity at the Big Bang.

New 4D strings

I found new formulations of the twistor superstring (of Nair; Witten; Roiban, Spradlin, and Volovich; and Berkovits) that allowed its generalization off-shell, and to a new string for which it is the tensionless limit. Andreev and I proposed strings that perturbatively exhibit both asymptotic freedom and the usual Regge behavior and spectrum.



My early work ('77-'83) involved mostly the use of superspace to treat supersymmetric theories, including supergravity. Gates, Grisaru, Roček, and I discovered methods for both deriving classical actions, and performing Feynman graph calculations more simply than those in nonsupersymmetric theories. I also found a new method of dimensional regularization ("dimensional reduction") which preserves supersymmetry, and is also commonly used in QCD.


In later work ('83-'88) I focused primarily on string theory. I invented (covariant) string field theory. With Zwiebach I generalized these methods outside of string theory to give a universal free field theory action for arbitrary representations of the Poincaré group in arbitrary dimensions. I also discovered new gauge symmetries of classical mechanics, useful for strings.



I spent a considerable portion of 1996-99 writing the book "Fields" --- the first free comprehensive (731 pages) textbook on quantum (and classical) field theory. I released the third edition (885 pages) in 2005 (available at, and am working on the fourth edition (1016 pages so far, available at my Web page, which has more details). It is published only electronically. Its approach to field theory is pragmatic, rather than traditional or artistic: It includes practical techniques, such as the 1/N expansion (color ordering) and spacecone (spinor helicity), and diverse topics, such as supersymmetry and general relativity, as well as introductions to supergravity and strings.

Other books

In 2001 I also released my 1988 book, "Introduction to String Field Theory," freely to the Web (e.g., at and, with the help of my coauthors S.J. Gates, M.T. Grisaru, and M. Roček, our 1983 standard, "Superspace, or One Thousand and One Lessons in Supersymmetry" (at

The program

Today most physics books (as well as almost all papers) are typeset in TeX. This makes it possible for any author to release his book for free, with no publishing costs to himself or the reader, should he so choose, either after a period of commercial sales (and return of copyright by the publisher) or immediately. Such electronic distribution of books is more convenient, cheaper, faster, and more ecologically friendly than paper books. In particular, the PDF versions of my books have Web links and clickable outline (contents) windows. My hope is that these books will help set new standards in both format and content that will make physics more accessible and relevant to students.


Complete publication list (196 last time I looked)
Preprints at
Past year



Hatsuda, Machiko S'90-S'91  Theory Division, KEK
Tsukuba, Ibaraki
305-0801, JAPAN
Eßler, Fabian S'91-S'93 Rudolf Peierls Centre for Theoretical Physics 
University of Oxford
1 Keble Road
Oxford, OX1 3NP, UK
Gasparakis, Charidimos F'91-F'95 electronics
Martinez, Mario F'92-S'94 (didn't finish Ph.D.)
Weiser, Harold F'92-F'99
Peeters, Bastiaan S'93-S'95 finance
Schalm, Koenraad F'95-S'99 Instituut-Lorentz for Theoretical Physics
University of Leiden
Leiden 2333CA, Netherlands
Biswas, Tirthabir F'00-S'03 Department of Physics
Loyola University
6363 St. Charles Avenue, Campus Box 92
New Orleans, LA 70118
Feng, Haidong F'03-S'07 finance
Lee, Kiyoung F'03-S'07 Owens Community College
P.O. Box 10,000
Toledo, Ohio 43699-1947
Martinez-Torteya, Carlos F'04-S'10 (didn't finish Ph.D.)
Huang, Yu-tin F'05-S'09 Department of Physics and Astronomy
National Taiwan University
Taipei 10617, Taiwan, ROC
Dai, Peng F'06-F'09 finance
Irizarry-Gelpí, Melvin Eloy F'08-S'13 Princeton, NJ
Jain, Dharmesh F'09-S'14 Department of Physics and Astronomy
National Taiwan University
Taipei 10617, Taiwan, ROC
Ju, Chia-Yi F'12-S'16 Taipei, Taiwan
Poláček, Martin F'13- Stony Brook

I also advised Aleksandar Miković and others at Maryland, and was the unofficial adviser of Jon Yamron and Nathan Berkovits at Berkeley.

COURSES TAUGHT @ Stony Brook (incl. lecture notes):

RelativityPHY 408S 95, 04
RelativityPHY 620S 92, 93, 96, 99, F 03, 05, 07
Quantum Field TheoryPHY 610-1    F 97-S 98, F 01-S 02, F 04-S 05, F 06-S 07, F 08-S 09, F 10-S 11, F 12-S 13
Advanced Quantum Field Theory    PHY 621    S 08, 10
String Theory (with others)PHY 622-3S-F 03, F 04-∞ (& beyond)




Univ. of California, Berkeley    6/70-12/72    A.B. Physics, Math.
Univ. of California, Berkeley 1/73- 6/77 Ph.D.    Physics



Harvard University 7/77-7/79    Honorary Postdoctoral Fellow
Brandeis University 3/79-6/79 Postdoctoral Fellow
Inst. for Advanced Study 8/79-8/80 Postdoctoral Fellow
Calif. Inst. of Technology 8/80-8/82 Postdoctoral Fellow
Univ. of Calif., Berkeley 8/82-8/85 Postdoctoral Fellow
Univ. of Md., College Park 8/85-6/87 Assistant Professor
" 7/87-9/88 Professor
State Univ. of N.Y., Stony Brook    9/88- Professor



C.N. Yang Institute for Theoretical Physics
State University of New York
Stony Brook, NY 11794-3840

Grant: NSF # PHY-1316617 (P.I.: G. Sterman)

Awards, consulting, professional affiliations: none

Local expert on some computer stuff: Mac, TeX, WWW, etc.