Shapiro-Virasoro amplitude and string field theory

Journal Article · Fri Jun 15 04:00:00 EDT 1990 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.41.3748· OSTI ID:6739058

Hua, L ^[1]; Kaku, M ^[2]

---

1. Physics Department, New York University, New York, New York 10003 (USA)
2. Institute for Advanced Study, Princeton, NJ (USA) Physics Department, City College of the City University of New York, NY (USA)

One of the embarrassments of covariant string field theory has been the glaring failure to derive the Shapiro-Virasoro amplitude. Modular invariance appears explicitly violated: either the fundamental region is overcounted an infinite number of times, or it is undercounted because of a missing region. We try to approach this problem from a fresh point of view. Conventional wisdom holds that, in string field theory, the Veneziano amplitude can only be derived either in light-cone string field theory or Witten's string field theory. We show that this firmly held belief is actually wrong, that the Veneziano amplitude can actually be derived using vertices of {ital arbitrary} lengths. This is a highly nontrivial calculation. Using third elliptic integrals we show that a series of miracles'' occurs which allow us to cancel scores of unwanted terms in the measure, leaving us with the correct Koba-Nielsen variable and measure. We give three independent proofs of our result. When we generalize our results to closed-string scattering with arbitrary lengths, we find a new surprise, that we can successfully derive the Shapiro-Virasoro amplitude as long as a crucial four-string interaction term is added. We check by explicit computer calculation that we reproduce the correct region of integration for the four-closed-string amplitude. Crucial to the theory is the existence of the missing four-string tetrahedron graph, which precisely fills the missing integration region. We comment on the implications of this for geometric string field theory.

• DOE Contract Number: AC02-76ER02220
• OSTI ID: 6739058
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 41:12; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
COMPOSITE MODELS
EXTENDED PARTICLE MODEL
FIELD THEORIES
LIGHT CONE
MATHEMATICAL MODELS
PARTICLE MODELS
PERTURBATION THEORY
QUARK MODEL
SCATTERING AMPLITUDES
SPACE-TIME
STRING MODELS
VENEZIANO MODEL