Ian Affleck,
Michael Dine, and Seiberg explored nonperturbative effects in supersymmetric field theories.[4] This work demonstrated, for the first time, that nonperturbative effects in four-dimensional field theories do not respect the
supersymmetry nonrenormalization theorems. This understanding led them to find four-dimensional models with dynamical
supersymmetry breaking.
In a series of papers,
Michael Dine and Seiberg explored various aspects of string theory. In particular, Dine,
Ryan Rohm, Seiberg, and
Edward Witten proposed a supersymmetry breaking mechanism based on gluino condensation,[5] Dine, Seiberg, and Witten showed that terms similar to
Fayet–Iliopoulos D-terms arise in string theory,[6] and Dine, Seiberg,
X. G. Wen, and Witten studied instantons on the string
worldsheet.[7]
Gregory Moore and Seiberg studied
Rational Conformal Field Theories. In the course of doing it, they invented modular tensor categories and described many of their properties.[8] They also explored the relation between Witten’s Topological
Chern–Simons theory and the corresponding Rational Conformal Field Theory.[9] This body of work was later used in mathematics and in the study of
topological phases of matter.
In the 90’s, Seiberg realized the significance of holomorphy as the underlying reason for the perturbative
supersymmetry nonrenormalization theorems[10] and initiated a program to use it to find exact results in complicated field theories including several N=1 supersymmetric
gauge theories in four dimension. These theories exhibit unexpected rich phenomena like confinement with and without chiral symmetry breaking and a new kind of electric-magnetic duality –
Seiberg duality.[11]Kenneth Intriligator and Seiberg studied many more models and summarized the subject in lecture notes.[12] Later, Intriligator, Seiberg and David Shih used this understanding of the dynamics to present four-dimensional models with dynamical supersymmetry breaking in a metastable vacuum.[13]
Seiberg and Witten studied the dynamics of four-dimensional N=2 supersymmetric theories –
Seiberg–Witten theory. They found exact expressions for several quantities of interest. These shed new light on interesting phenomena like confinement, chiral symmetry breaking, and electric-magnetic duality.[14] This insight was used by Witten to derive the
Seiberg–Witten invariants. Later, Seiberg and Witten extended their work to the four-dimensional N=2 theory compactified to three dimensions.[15]
Intriligator and Seiberg found a new kind of duality in three-dimensional N=4 supersymmetric theories, which is reminiscent of the well-known
2D mirror symmetry –
3D mirror symmetry.[16]
In a series of papers with various collaborators, Seiberg studied many supersymmetric theories in three, four, five, and six dimensions. The three-dimensional N=2 supersymmetric theories[17] and their dualities were shown to be related to the four-dimensional N=1 theories.[18] And surprising five-dimensional theories with N=2 supersymmetries were discovered[19] and analyzed.[20]
As part of his work on the
BFSS matrix model, Seiberg discovered
little string theories.[21] These are limits of string theory without gravity that are not local quantum field theories.
Seiberg and Witten identified a particular low-energy limit (Seiberg–Witten limit) of theories containing
open strings in which the dynamics becomes that of
noncommutative quantum field theory – a field theory on a
non-commutative geometry. They also presented a map (
Seiberg–Witten map) between standard gauge theories and gauge theories on a noncommutative space.[22]Shiraz Minwalla,
Mark Van Raamsdonk and Seiberg uncovered a surprising mixing between short-distance and long-distance phenomena in these field theories on a noncommutative space. Such mixing violates the standard picture of the renormalization group. They referred to this phenomenon as UV/IR mixing.[23]
Davide Gaiotto,
Anton Kapustin, Seiberg, and Brian Willett introduced the notion of higher-form global symmetries and studied some of their properties and applications.[24]
^Seiberg, “Exact results on the space of vacua of four-dimensional SUSY gauge theories”, hep-th/9402044, {{DOI:10.1103/PhysRevD.49.6857}}, Phys.Rev.D 49 (1994), 6857-6863; “Electric - magnetic duality in supersymmetric non-Abelian gauge theories”, hep-th/9411149, {{DOI: 10.1016/0550-3213(94)00023-8}}, Nucl.Phys.B 435 (1995), 129-146.
^Intriligator and Seiberg “Lectures on supersymmetric gauge theories and electric-magnetic duality” Nucl.Phys.B Proc.Suppl. 45BC (1996), 1-28, Subnucl.Ser. 34 (1997), 237-299, {{ DOI: 10.1016/0920-5632(95)00626-5}}, hep-th/9509066
^Intriligator, Seiberg, and Shih, “Dynamical SUSY breaking in meta-stable vacua”, hep-th/0602239 [hep-th], JHEP 04 (2006), 021, {{DOI: 10.1088/1126-6708/2006/04/021}}
^Seiberg and Witten, “Electric - magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory”{{ DOI: 10.1016/0550-3213(94)90124-4 , 10.1016/0550-3213(94)00449-8 (erratum)}}, Nucl.Phys.B 426 (1994), 19-52, Nucl.Phys.B 430 (1994), 485-486 (erratum), hep-th/9407087; “Monopoles, duality and chiral symmetry breaking in N=2 supersymmetric QCD”, Nucl.Phys.B 431 (1994), 484-550, {{DOI: 10.1016/0550-3213(94)90214-3}}, hep-th/9408099.
^Seiberg and Witten, “Gauge dynamics and compactification to three-dimensions”, hep-th/9607163, in “Conference on the Mathematical Beauty of Physics (In Memory of C. Itzykson)”.
^Aharony, Hanany, Intriligator, and Seiberg, “Aspects of N=2 supersymmetric gauge theories in three-dimensions”, hep-th/9703110, Nucl.Phys.B 499 (1997), 67-99, {{DOI: 10.1016/S0550-3213(97)00323-4}}
^Aharony, Razamat, Seiberg, and Willett, “3d dualities from 4d dualities”, hep-th/1305.3924, {{DOI: 10.1007/JHEP07(2013)149}}, JHEP 07 (2013), 149
^Seiberg, “Five-dimensional SUSY field theories, nontrivial fixed points and string dynamics”, hep-th/9608111 {{DOI: 10.1016/S0370-2693(96)01215-4}}, Phys.Lett.B 388 (1996), 753-760
^Morrison and Seiberg, “Extremal transitions and five-dimensional supersymmetric field theories”, hep-th/9609070, {{DOI: 10.1016/S0550-3213(96)00592-5}}, Nucl.Phys.B 483 (1997), 229-247; Intriligator, Morrison, and Seiberg, “Five-dimensional supersymmetric gauge theories and degenerations of Calabi-Yau spaces”, hep-th/9702198, {{DOI: 10.1016/S0550-3213(97)00279-4}}, Nucl.Phys.B 497 (1997), 56-100.
^Seiberg “New theories in six-dimensions and matrix description of M theory on T**5 and T**5 / Z(2)” hep-th/9705221,{{DOI: 10.1016/S0370-2693(97)00805-8}} Phys.Lett.B 408 (1997), 98-104
^Seiberg and Witten “String theory and noncommutative geometry”, JHEP 09 (1999), 032, In *Li, M. (ed.) et al.: Physics in non-commutative world* 327-401, hep-th/9908142, {{DOI:10.1088/1126-6708/1999/09/032}}.
^Minwalla, Van Raamsdonk, and Seiberg, “Noncommutative perturbative dynamics”, JHEP 02 (2000), 020, In *Li, M. (ed.) et al.: Physics in non-commutative world* 426-451, hep-th/9912072, {{DOI: 10.1088/1126-6708/2000/02/020}}
Ian Affleck,
Michael Dine, and Seiberg explored nonperturbative effects in supersymmetric field theories.[4] This work demonstrated, for the first time, that nonperturbative effects in four-dimensional field theories do not respect the
supersymmetry nonrenormalization theorems. This understanding led them to find four-dimensional models with dynamical
supersymmetry breaking.
In a series of papers,
Michael Dine and Seiberg explored various aspects of string theory. In particular, Dine,
Ryan Rohm, Seiberg, and
Edward Witten proposed a supersymmetry breaking mechanism based on gluino condensation,[5] Dine, Seiberg, and Witten showed that terms similar to
Fayet–Iliopoulos D-terms arise in string theory,[6] and Dine, Seiberg,
X. G. Wen, and Witten studied instantons on the string
worldsheet.[7]
Gregory Moore and Seiberg studied
Rational Conformal Field Theories. In the course of doing it, they invented modular tensor categories and described many of their properties.[8] They also explored the relation between Witten’s Topological
Chern–Simons theory and the corresponding Rational Conformal Field Theory.[9] This body of work was later used in mathematics and in the study of
topological phases of matter.
In the 90’s, Seiberg realized the significance of holomorphy as the underlying reason for the perturbative
supersymmetry nonrenormalization theorems[10] and initiated a program to use it to find exact results in complicated field theories including several N=1 supersymmetric
gauge theories in four dimension. These theories exhibit unexpected rich phenomena like confinement with and without chiral symmetry breaking and a new kind of electric-magnetic duality –
Seiberg duality.[11]Kenneth Intriligator and Seiberg studied many more models and summarized the subject in lecture notes.[12] Later, Intriligator, Seiberg and David Shih used this understanding of the dynamics to present four-dimensional models with dynamical supersymmetry breaking in a metastable vacuum.[13]
Seiberg and Witten studied the dynamics of four-dimensional N=2 supersymmetric theories –
Seiberg–Witten theory. They found exact expressions for several quantities of interest. These shed new light on interesting phenomena like confinement, chiral symmetry breaking, and electric-magnetic duality.[14] This insight was used by Witten to derive the
Seiberg–Witten invariants. Later, Seiberg and Witten extended their work to the four-dimensional N=2 theory compactified to three dimensions.[15]
Intriligator and Seiberg found a new kind of duality in three-dimensional N=4 supersymmetric theories, which is reminiscent of the well-known
2D mirror symmetry –
3D mirror symmetry.[16]
In a series of papers with various collaborators, Seiberg studied many supersymmetric theories in three, four, five, and six dimensions. The three-dimensional N=2 supersymmetric theories[17] and their dualities were shown to be related to the four-dimensional N=1 theories.[18] And surprising five-dimensional theories with N=2 supersymmetries were discovered[19] and analyzed.[20]
As part of his work on the
BFSS matrix model, Seiberg discovered
little string theories.[21] These are limits of string theory without gravity that are not local quantum field theories.
Seiberg and Witten identified a particular low-energy limit (Seiberg–Witten limit) of theories containing
open strings in which the dynamics becomes that of
noncommutative quantum field theory – a field theory on a
non-commutative geometry. They also presented a map (
Seiberg–Witten map) between standard gauge theories and gauge theories on a noncommutative space.[22]Shiraz Minwalla,
Mark Van Raamsdonk and Seiberg uncovered a surprising mixing between short-distance and long-distance phenomena in these field theories on a noncommutative space. Such mixing violates the standard picture of the renormalization group. They referred to this phenomenon as UV/IR mixing.[23]
Davide Gaiotto,
Anton Kapustin, Seiberg, and Brian Willett introduced the notion of higher-form global symmetries and studied some of their properties and applications.[24]
^Seiberg, “Exact results on the space of vacua of four-dimensional SUSY gauge theories”, hep-th/9402044, {{DOI:10.1103/PhysRevD.49.6857}}, Phys.Rev.D 49 (1994), 6857-6863; “Electric - magnetic duality in supersymmetric non-Abelian gauge theories”, hep-th/9411149, {{DOI: 10.1016/0550-3213(94)00023-8}}, Nucl.Phys.B 435 (1995), 129-146.
^Intriligator and Seiberg “Lectures on supersymmetric gauge theories and electric-magnetic duality” Nucl.Phys.B Proc.Suppl. 45BC (1996), 1-28, Subnucl.Ser. 34 (1997), 237-299, {{ DOI: 10.1016/0920-5632(95)00626-5}}, hep-th/9509066
^Intriligator, Seiberg, and Shih, “Dynamical SUSY breaking in meta-stable vacua”, hep-th/0602239 [hep-th], JHEP 04 (2006), 021, {{DOI: 10.1088/1126-6708/2006/04/021}}
^Seiberg and Witten, “Electric - magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory”{{ DOI: 10.1016/0550-3213(94)90124-4 , 10.1016/0550-3213(94)00449-8 (erratum)}}, Nucl.Phys.B 426 (1994), 19-52, Nucl.Phys.B 430 (1994), 485-486 (erratum), hep-th/9407087; “Monopoles, duality and chiral symmetry breaking in N=2 supersymmetric QCD”, Nucl.Phys.B 431 (1994), 484-550, {{DOI: 10.1016/0550-3213(94)90214-3}}, hep-th/9408099.
^Seiberg and Witten, “Gauge dynamics and compactification to three-dimensions”, hep-th/9607163, in “Conference on the Mathematical Beauty of Physics (In Memory of C. Itzykson)”.
^Aharony, Hanany, Intriligator, and Seiberg, “Aspects of N=2 supersymmetric gauge theories in three-dimensions”, hep-th/9703110, Nucl.Phys.B 499 (1997), 67-99, {{DOI: 10.1016/S0550-3213(97)00323-4}}
^Aharony, Razamat, Seiberg, and Willett, “3d dualities from 4d dualities”, hep-th/1305.3924, {{DOI: 10.1007/JHEP07(2013)149}}, JHEP 07 (2013), 149
^Seiberg, “Five-dimensional SUSY field theories, nontrivial fixed points and string dynamics”, hep-th/9608111 {{DOI: 10.1016/S0370-2693(96)01215-4}}, Phys.Lett.B 388 (1996), 753-760
^Morrison and Seiberg, “Extremal transitions and five-dimensional supersymmetric field theories”, hep-th/9609070, {{DOI: 10.1016/S0550-3213(96)00592-5}}, Nucl.Phys.B 483 (1997), 229-247; Intriligator, Morrison, and Seiberg, “Five-dimensional supersymmetric gauge theories and degenerations of Calabi-Yau spaces”, hep-th/9702198, {{DOI: 10.1016/S0550-3213(97)00279-4}}, Nucl.Phys.B 497 (1997), 56-100.
^Seiberg “New theories in six-dimensions and matrix description of M theory on T**5 and T**5 / Z(2)” hep-th/9705221,{{DOI: 10.1016/S0370-2693(97)00805-8}} Phys.Lett.B 408 (1997), 98-104
^Seiberg and Witten “String theory and noncommutative geometry”, JHEP 09 (1999), 032, In *Li, M. (ed.) et al.: Physics in non-commutative world* 327-401, hep-th/9908142, {{DOI:10.1088/1126-6708/1999/09/032}}.
^Minwalla, Van Raamsdonk, and Seiberg, “Noncommutative perturbative dynamics”, JHEP 02 (2000), 020, In *Li, M. (ed.) et al.: Physics in non-commutative world* 426-451, hep-th/9912072, {{DOI: 10.1088/1126-6708/2000/02/020}}