A finite representation for a superstring scattering amplitude and its low-energy limit

Montag, J. Lee; Weisberger, William

doi:10.1016/0550-3213(91)80031-g

Cited by 15 publications

(38 citation statements)

References 6 publications

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“…Such an analytic continuation relevant to the four point superstring amplitude of massless states at one loop has been done in [13,14]. We describe below the details of the analytic continuation in the present case.…”

Section: Analytic Continuationmentioning

confidence: 99%

Non-renormalization of mass of some non-supersymmetric string states

1998

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Section: Analytic Continuationmentioning

confidence: 99%

Non-renormalization of mass of some non-supersymmetric string states

1998

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“…Early attempts to implement this achieved only partial success [1,2]. A systematic method of dealing with this was suggested in [4][5][6] (see also [9,10]). This was achieved by considering a four point amplitude with external momenta chosen in appropriate range where the integrals are well defined, then analytically continuing the result to the physical region where we expect a pole due to the massive particle of interest, and finally finding the shift in mass 2 from the location of the pole.…”

Section: Jhep11(2016)050mentioning

confidence: 99%

One loop mass renormalization of unstable particles in superstring theory

Sen

2016

J. High Energ. Phys.

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Most of the massive states in superstring theory are expected to undergo mass renormalization at one loop order. Typically these corrections should contain imaginary parts, indicating that the states are unstable against decay into lighter particles. However in such cases, direct computation of the renormalized mass using superstring perturbation theory yields divergent result. Previous approaches to this problem involve various analytic continuation techniques, or deforming the integral over the moduli space of the torus with two punctures into the complexified moduli space near the boundary. In this paper we use insights from string field theory to describe a different approach that gives manifestly finite result for the mass shift satisfying unitarity relations. The procedure is applicable to all states of (compactified) type II and heterotic string theories. We illustrate this by computing the one loop correction to the mass of the first massive state on the leading Regge trajectory in SO(32) heterotic string theory.

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“…We may now write down the expansions of (C. [8][9][10][11] in terms of the expansion coefficients T and T * . First for the monomial terms only…”

Section: Heterotic Superstringsmentioning

confidence: 99%

“…In §III, we divide up the integration over moduli of the torus -including the positions of the vertex operators -into 3 inequivalent regions which transform into one another under duality [11,14]. We exhibit a formal equivalence of the amplitudes with an infinite sum over φ 3 quantum field theory box diagrams in which each propagator can have a different mass.…”

Section: Introductionmentioning

confidence: 99%

“…Following the rules of Lorentz covariant superstring perturbation theory, one finds a one-loop amplitude represented by an integral over the positions of vertex operators of incoming and outgoing states and moduli on the torus [1,2,8,9]. This representation is modular invariant, but the integral appears to be absolutely convergent only when the Mandelstam variables s, t and u are all purely imaginary [7,10,11]. For real external momenta and in fact for any values of s, t and u that are not purely imaginary, it is easy to see that the integral is real and infinite [7,12].…”

Section: Introductionmentioning

confidence: 99%

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The box graph in superstring theory

D’Hoker

Phong

1995

Nuclear Physics B

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In theories of closed oriented superstrings, the one loop amplitude is given by a single diagram, with the topology of a torus. Its interpretation had remained obscure, because it was formally real, converged only for purely imaginary values of the Mandelstam variables, and had to account for the singularities of both the box graph and the one particle reducible graphs in field theories. We present in detail an analytic continuation method which resolves all these difficulties. It is based on a reduction to certain minimal amplitudes which can themselves be expressed in terms of double and single dispersion relations, with explicit spectral densities. The minimal amplitudes correspond formally to an infinite superposition of box graphs on φ 3 like field theories, whose divergence is responsible for the poles in the string amplitudes.

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A finite representation for a superstring scattering amplitude and its low-energy limit

Cited by 15 publications

References 6 publications

Non-renormalization of mass of some non-supersymmetric string states

Non-renormalization of mass of some non-supersymmetric string states

One loop mass renormalization of unstable particles in superstring theory

The box graph in superstring theory

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