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String field theory (SFT) is a formalism in string theory in which the dynamics of relativistic strings is reformulated in the language of quantum field theory. This is accomplished at the level of perturbation theory by finding a collection of vertices for joining and splitting strings, as well as string propagators, that give a Feynman diagram-like expansion for string scattering amplitudes. In most string field theories, this expansion is encoded by a classical action found by second-quantizing the free string and adding interaction terms. As is usually the case in second quantization, a classical field configuration of the second-quantized theory is given by a wave function in the original theory. In the case of string field theory, this implies that a classical configuration, usually called the string field, is given by an element of the free string Fock space. The principal advantages of the formalism are that it allows the computation of off-shell amplitudes and, when a classical action is available, gives non-perturbative information that cannot be seen directly from the standard genus expansion of string scattering. In particular, following the work of Ashoke Sen,〔A. Sen, "Universality of the tachyon potential", JHEP 9912:027, (1999)〕 it has been useful in the study of tachyon condensation on unstable D-branes. It has also had applications to topological string theory,〔E. Witten, "Chern–Simons gauge theory as a string theory", Prog. Math. 133 637, (1995)〕 non-commutative geometry,〔E. Witten, "Noncommutative tachyons and string field theory", hep-th/0006071〕 and strings in low dimensions.〔D. Gaiotto and L. Rastelli, "A Paradigm of open/closed duality: Liouville D-branes and the Kontsevich model", JHEP 0507:053, (2005)〕 String field theories come in a number of varieties depending on which type of string is second quantized: ''Open string field theories'' describe the scattering of open strings, ''closed string field theories'' describe closed strings, while ''open-closed string field theories'' include both open and closed strings. In addition, depending on the method used to fix the worldsheet diffeomorphisms and conformal transformations in the original free string theory, the resulting string field theories can be very different. Using light cone gauge, yields ''light-cone string field theories'' whereas using BRST quantization, one finds ''covariant string field theories''. There are also hybrid string field theories, known as ''covariantized light-cone string field theories'' which use elements of both light-cone and BRST gauge-fixed string field theories.〔H. Hata, K. Itoh, T. Kugo, H. Kunitomo, and K. Ogawa, "Manifestly Covariant Field Theory of Interacting String." Phys.Lett. B172 (1986) 186.〕 A final form of string field theory, known as ''background independent open string field theory'', takes a very different form; instead of second quantizing the worldsheet string theory, it second quantizes the space of two-dimensional quantum field theories.〔E. Witten, "On background independent open string field theory." Phys.Rev. D46 (1992) 5467.〕 == Light-cone string field theory == Light-cone string field theories were introduced by Stanley Mandelstam〔S. Mandelstam, "Interacting String Picture of The Dual Resonance Models," Nucl. Phys. B64 , 205 (1973); S. Mandelstam, "Interacting String Picture of The Neveu–Schwarz–Ramond Model," Nucl. Phys. B69 , 77 (1974);〕 and developed by Mandelstam, Michael Green, John Schwarz and Lars Brink.〔 M. B. Green and J. H. Schwarz, “Supersymmetrical Dual String Theory. 2. Vertices And Trees,” Nucl. Phys. B198, 252 (1982); M. B. Green and J. H. Schwarz, "Superstring Interactions," Nucl. Phys. B218 , 43 (1983); M. B. Green, J. H. Schwarz and L. Brink, “Superfield Theory Of Type II Superstrings,” Nucl. Phys. B 219, 437 (1983); M. B. Green and J. H. Schwarz, “Superstring Field Theory,” Nucl. Phys. B243 , 475 (1984); S. Mandelstam, "Interacting String Picture Of The Fermionic String," Prog. Theor. Phys. Suppl. 86 , 163 (1986); 〕 An explicit description of the second-quantization of the light-cone string was given by Michio Kaku and Keiji Kikkawa.〔Michio Kaku and K. Kikkawa, "Field theory of relativistic strings. I. Trees", Phys. Rev. D10, 1110 (1974); Michio Kaku and K. Kikkawa, "The Field Theory of Relativistic Strings. 2. Loops and Pomerons", Phys.Rev. D10,1823,(1974). 〕 Light-cone string field theories were the first string field theories to be constructed and are based on the simplicity of string scattering in light-cone gauge. For example, in the bosonic closed string case, the worldsheet scattering diagrams naturally take a Feynman diagram-like form, being built from two ingredients, a propagator, :: and two vertices for splitting and joining strings, which can be used to glue three propagators together, :: These vertices and propagators produce a single cover of the moduli space of -point closed string scattering amplitudes so no higher order vertices are required.〔E. D’Hoker and S. B. Giddings, “Unitarity Of The Closed Bosonic Polyakov String,” Nucl. Phys. B291 (1987) 90.〕 Similar vertices exist for the open string. When one considers light-cone quantized ''superstrings'', the discussion is more subtle as divergences can arise when the light-cone vertices collide.〔J. Greensite and F. R. Klinkhamer, “New Interactions For Superstrings,” Nucl. Phys. B281 (1987) 269〕 To produce a consistent theory, it is necessary to introduce higher order vertices, called contact terms, to cancel the divergences. Light-cone string field theories have the disadvantage that they break manifest Lorentz invariance. However, in backgrounds with light-like killing vectors, they can considerably simplify the quantization of the string action. Moreover, until the advent of the Berkovits string〔N. Berkovits, "Super Poincare covariant quantization of the superstring", JHEP 0004:018, (2000).〕 it was the only known method for quantizing strings in the presence of Ramond–Ramond fields. In recent research, light-cone string field theory played an important role in understanding strings in pp-wave backgrounds.〔M. Spradlin and A. Volovich, "Light-cone string field theory in a plane wave", Lectures given at ICTP Spring School on Superstring Theory and Related Topics, Trieste, Italy, 31 Mar – 8 Apr (2003) hep-th/0310033.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「String field theory」の詳細全文を読む スポンサード リンク
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