Abstract
I give an introductory review of recent, fascinating developments in supersymmetric gauge theories. I explain pedagogically the miraculous properties of supersymmetric gauge dynamics allowing one to obtain exact solutions in many instances. Various dynamical regimes emerging in supersymmetric Quantum Chromodynamics and its generalizations are discussed. I emphasize those features that have a chance of survival in QCD and those which are drastically different in supersymmetric and non-supersymmetric gauge theories. Unlike most of the recent reviews focusing almost entirely on the progress in extended supersymmetries (the Seiberg-Witten solution of N=2 models), these lectures are mainly devoted to N=1 theories. Developments “after Seiberg” (domain walls in supersymmetric gluodynamics) are briefly discussed.
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References
A. Polyakov, Nucl. Phys. B120 (1977) 429.
S. Mandelstam, Phys. Reports 23 (1976) 245.
G. ’t Hooft, in 1981 Cargése Summer School Lecture Notes on Fundamental Interactions, NATO Adv. Study Inst. Series B: Phys., Vol. 85, ed. M. Lévy et al. (Plenum Press, New York, 1982) [reprinted in G.’ t Hooft, Under the Spell of the Gauge Principle (World Scientific, Singapore, 1994), page 514]; Nucl. Phys. B190 (1981) 455.
Yu. Golfand and E. Likhtman, Pis’ma ZhETF, 13 (1971) 452 [JETP Lett. 13 (1971) 323]; see also in Problems of Theoretical Physics, I.E. Tamm Memorial Volume (Nauka, Moscow, 1972), page 37; E.P. Likhtman, Irreducible representations, extensions of the algebra of Poincaré. generators by bispinor generators, Kratk. Soob. Fiz. — Short Comm. Phys. FIAN, 1971, No. 5, page 197.
J. Wess and B. Zumino, Nucl. Phys. B70 (1974) 39; Phys. Lett. B49 (1974) 52.
W. Pauli, Pauli Lectures on Physics, Vol. 6, Selected Topics in Field Quantization (MIT Press, Cambridge, 1973), page 33.
A. Salam and J. Strathdee, Nucl. Phys. B76 (1974) 477; Phys. Rev. D11 (1975) 1521.
S. Ferrara and B. Zumino, Nucl. Phys. B79 (1974) 413.
V. Novikov, M. Shifman, A. Vainshtein and V. Zakharov, Nucl. Phys. B229 (1983) 407.
M. Shifman and A. Vainshtein, Nucl. Phys. B296 (1988) 445.
A. Kovner and M. Shifman, Phys. Rev. D56 (1997) 2396.
G. Veneziano and S. Yankielowicz, Phys. Lett. B113 (1982) 321; T. R. Taylor, G. Veneziano and S. Yankielowicz, Nucl. Phys. B218 (1983) 493.
V. Novikov, M. Shifman, A. Vainshtein and V. Zakharov, Nucl.Phys. B229 (1983) 381; Phys. Lett. B166 (1986) 334.
A. Salam and J. Strathdee, Nucl. Phys. B87 (1975) 85; P. Fayet, Nucl. Phys. B90 (1975) 104.
M. Grisaru, in Recent Developments in Gravitation (Cargése Lectures, 1978), Eds. M. Levy and S. Deser (Plenum Press, New York, 1979), page 577, and references therein.
E. Witten, Nucl. Phys. B202 (1982) 253.
F. Buccella, J.-P. Derendinger, C. Savoy and S. Ferrara, Phys. Lett. B115 (1982) 375, and in Proc. Europhys. Study Conf. Unification of the Fundamental Particle Interactions. II, Eds. J. Ellis and S. Ferrara (Plenum Press, New York, 1983), page 349.
I. Affleck, M. Dine and N. Seiberg, Nucl. Phys. B241 (1984) 493.
I. Affleck, M. Dine and N. Seiberg, Nucl. Phys. B256 (1985) 557.
M. Luty and W. Taylor, Phys. Rev. D53 (1996) 3399.
J. Bagger and J. Wess, Supersymmetry and Supergravity, 2nd Edition (Princeton University Press, Princeton, 1992).
E. Witten, Nucl. Phys. B403 (1993) 159.
A. Vainshtein, V. Zakharov and M. Shifman, Usp. Fiz. Nauk, 146 (1985) 683 [Sov. Phys.-. Usp. 28 (1985) 709].
I. Kogan, A. Morozov, M. Olshanetsky and M. Shifman, Yad. Fiz. 43 (1986) 1587 [Sov. J. Nucl. Phys. 43 (1986) 1022].
N. Seiberg, Phys. Rev. D49 (1994) 6857; Nucl. Phys. B435 (1995) 129.
K. Intriligator and N. Seiberg, Nucl. Phys. B431 (1994) 551; K. Intriligator, R. Leigh, and N. Seiberg, Phys. Rev. D50 (1994) 1092.
K. Intriligator, R. Leigh, and M. Strassler, Nucl. Phys. B456 (1995) 567.
E. Poppitz and L. Randall, Phys. Lett. B336 (1994) 402; J. Bagger, E. Poppitz and L. Randall, Nucl. Phys. B426 (1994) 3.
S. Giddings and J.M. Pierre, Phys. Rev. D52 (1995) 6065.
T. Gherghetta, C. Kolda and S. Martin, Nucl. Phys. B468 (1996) 37.
J. Wess and B. Zumino, Phys. Lett. B49 (1974) 52; J. Iliopoulos and B. Zumino, Nucl. Phys. B76 (1974) 310; P. West, Nucl. Phys. B106 (1976) 219; M. Grisaru, M. Roček, and W. Siegel, Nucl. Phys. B159 (1979) 429.
Y. Meurice and G. Veneziano, Phys. Lett. B141 (1984) 69; I. Affleck, M. Dine and N. Seiberg, Phys. Lett. B137 (1984) 187.
D. Amati, K. Konishi, Y. Meurice, G. Rossi and G. Veneziano, Phys. Rep. 162 (1988) 557.
I. Affleck, M. Dine and N. Seiberg, Phys. Rev. Lett. 52 (1984) 1677; Y. Meurice and G. Veneziano, Phys. Lett. B141 (1984) 69.
S. Ferrara and B. Zumino, Nucl. Phys. B87 (1975) 207.
M. Shifman and A. Vainshtein, Nucl. Phys. B277 (1986) 456.
I. Kogan, M. Shifman, and A. Vainshtein, Phys. Rev. D53 (1996) 4526.
J. Wess and B. Zumino, Phys. Lett. B49 (1974) 52.
M. Shifman and A. Vainshtein, Nucl. Phys. B359 (1991) 571.
I. Jack, D.R.T. Jones, and P. West, Phys. Lett. B258 (1991) 382.
E. Poppitz and L. Randall, Phys. Lett. B389 (1996) 280.
T.E. Clark, O. Piguet, and K. Sibold, Nucl. Phys. B159 (1979) 1; K. Konishi, Phys. Lett. B135 (1984) 439; K. Konishi and K. Shizuya, Nuov. Cim. A90 (1985) 111.
V. Novikov, M. Shifman, A. Vainshtein and V. Zakharov, Nucl. Phys. B260 (1985) 157; for a review see23.
A. Vainshtein, V. Zakharov and M. Shifman, Yad. Fiz. 43 (1986) 1596 [Sov. J. Nucl. Phys. 43 (1986) 1028], Sect. 3; see also Pis’ma ZhETF 42 (1985) 182 [JETP Lett. 42 (1985) 224]; for a recent discussion see M. Shifman, Int. J. Mod. Phys. A11 (1996) 5761.
I. Jack, D.R.T. Jones and C.G. North, Nucl. Phys. B486 (1997) 479.
N. Seiberg, Phys. Lett. 206B (1988) 75.
N. Seiberg, Phys. Lett. B318 (1993) 469.
I. Affleck, M. Dine and N. Seiberg, Phys. Rev. Lett. 51 (1983) 1026.
I. Affleck, M. Dine and N. Seiberg, Phys. Lett. B137 (1984) 187; Phys. Rev. Lett. 52 (1984) 493; Phys. Lett. B140 (1984) 59.
L. Dixon, V. Kaplunovsky and J. Louis, Nucl. Phys. B355 (1991) 649.
H. Li and K. Mahanthappa, Phys. Lett. B319 (1993) 152; Phys. Rev. D49 (1994) 5532.
M. Shifman (Ed.), Instantons in Gauge Theories (World Scientific, Singapore, 1994), Chapter VII.
B. Zumino, Phys. Lett. B69 (1977) 369.
A. D’Adda and P. Di Vecchia, Phys. Lett. B73 (1978) 162.
G.C. Rossi and G. Veneziano, Phys. Lett. B138 (1984) 195.
N. Seiberg and E. Witten, Nucl. Phys. B426 (1994) 19; (E) B430 (1994) 485; Nucl. Phys. B431 (1994) 484.
N. Dorey, V. Khoze, and M. Mattis, Phys. Rev, D54 (1996) 2921; Phys. Rev. D54 (1996) 7832; Phys. Lett. B388 (1996) 324; Phys. Lett. B390 (1997) 205; H. Aoyama, T. Harano, M. Sato, and S. Wada, Phys. Lett. B388 (1996) 331; K. Ito and N. Sasakura, Nucl. Phys. B484 (1997) 141; Mod. Phys. Lett. A12 (1997) 205; F. Fucito and T. Travaglini, Phys. Rev. D55 (1997) 1099; T. Harano and M. Sato, Nucl. Phys. B484 (1997) 167; Y. Yoshida, hep-th/9610211; M. Slater, Phys. Lett. B403 (1997) 57.
A. Yung, Nucl. Phys. B485 (1997) 38.
S. Dimopoulos, Nucl. Phys. B168 (1980) 69; M. Peskin, Nucl. Phys. B175 (1980) 197.
M. Vysotsky, I. Kogan, and M. Shifman, Yad. Fiz. 42 (1985) 504 [Sov. J. Nucl. Phys. 42 (1985) 318].
A.C. Davis, M. Dine and N. Seiberg, Phys. Lett. B125 (1983) 487.
G. ’t Hooft, in Recent Developments in Gauge Theories, Eds. G. ’t Hooft et at., (Plenum Press, New York, 1980).
A. Dolgov and V. Zakharov, Nucl. Phys. B12 (1971) 68.
M. Shifman, Phys. Rep. 209 (1991) 161.
C. Vafa and E. Witten, Nucl. Phys. B234 (1984) 173.
S. Coleman and E. Witten, Phys. Rev. Lett. 45 (1980) 100.
E. Poppitz and S. Trivedi, Phys. Lett. B365 (1996) 125; P. Pouliot, Phys. Lett. B367 (1996) 151.
K. Intriligator and P. Pouliot, Phys. Lett. B353 (1996) 471.
P. Cho and P. Kraus, Phys. Rev. D54 (1996) 7640.
C. Csáki, W. Skiba and M. Schmaltz, Nucl. Phys. B487 (1997) 128.
K. Intriligator and N. Seiberg, Nucl. Phys. B444 (1995) 125.
P. Pouliot, Phys. Lett. B359 (1995) 108; P. Pouliot and M. Strassler, Phys. Lett. B370 (1996) 76; Phys. Lett. B375 (1996) 175.
I. Pesando, Mod. Phys. Lett. A10 (1995) 1871; S. Giddings and J. Pierre, Phys. Rev. D52 (1995) 6065.
C. Csáki, M. Schmaltz, and W. Skiba, Phys. Rev. Lett. 78 (1997) 799; Phys. Rev. D55 (1997) 7840.
For a concise review and relevant references see e.g. I. Hinchliffe, Phys. Rev. D54 (1996) 77.
A. Belavin and A. Migdal, Pis’ma ZhETF 19 (1974) 317 [JETP Lett. 19 (1974) 181]; Scale. Invariance and Bootstrap in the Non-Abelian Gauge Theories, Landau Institute Preprint-74-0894, 1974 (unpublished).
T. Banks and Zaks, Nucl. Phys. B196 (1982) 189.
N. Seiberg, Nucl. Phys. B435 (1995) 129.
D. Kutasov, A. Schwimmer, and N. Seiberg, Nucl. Phys. B459 (1996) 455.
G. ’t Hooft, Phys. Rev. D14 (1976) 3432; (E) D18 (1978) 2199.
P. Pouliot, Phys. Lett. B359 (1995) 108; D. Kutasov, Phys. Lett. B351 (1995) 230; D. Kutasov and A. Schwimmer, Phys. Lett. B354 (1995) 315; P. Pouliot and M. Strassler, Phys. Lett. B370 (1996) 76; B375 (1996) 175; K. Intriligator, Nucl. Phys. B448 (1995) 187; K. Intriligator, R. Leigh and M. Strassler, Nucl. Phys. B456 (1995) 567.
J. Distler and A. Karch, hep-th/9611088.
J. Brodie and M. Strassler, hep-th/9611197; P. Cho, Phys. Rev. D56 (1997) 5260; and references therein.
G. Dvali and M. Shifman, Phys. Lett. B396 (1997) 64; (E) B407 (1997) 452.
R. Haag, J. Lopuszanski and M. Sohnius, Nucl. Phys. B88 (1975) 257.
S. Coleman and J. Mandula, Phys. Rev. 159 (1967) 1251.
E. Witten and D. Olive, Phys. Lett. B78 (1978) 97.
S. Ferrara and B. Zumino, Nucl. Phys. B87 (1975) 207.
B. Chibisov and M. Shifman, hep-th/9706089 [Phys. Rev. D, to appear).
E. Bogomol’nyi, Sov. J. Nucl. Phys. 24 (1976) 449, M.K. Prasad and C.H. Sommerfield, Phys. Rev. Lett. 35 (1976) 760.
G. Dvali and M. Shifman, hep-th/9611213 [Nucl. Phys. B, to appear].
M. Shifman, hep-th/9708060 [Phys. Rev. D, submitted]; M. Shifman and M. Voloshin, hep-th/9709137 [Phys. Rev. D, submitted].
A. Kovner, M. Shifman and A. Smilga, hep-th/9706089 [Phys. Rev. D, submitted]; A. Smilga and A. Veselov, hep-th/9710123.
E. Witten, hep-th/9706109.
V.B. Berestetskii, E.M, Lifshits and L.P. Pitaevskii, Quantum Electrodynamics, (Pergamon Press, New York, 1982).
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Shifman, M. (2002). Non-Perturbative Gauge Dynamics in Supersymmetric Theories. A Primer. In: van Baal, P. (eds) Confinement, Duality, and Non-Perturbative Aspects of QCD. NATO Science Series: B:, vol 368. Springer, Boston, MA. https://doi.org/10.1007/0-306-47056-X_18
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