Multiloop String Amplitudes with B-Field and Noncommutative QFT

Abstract

The multiloop amplitudes for the bosonic string in presence of a constant B-field are built by using the basic commutation relations for the open string zero modes and oscillators. The open string Green function on the annulus is obtained from the one loop scattering amplitude among N tachyons. For higher loops, it is necessary to use the so called three Reggeon vertex, which describes the emission from the open string of another string and not simply of a tachyon. We find that the modifications to the three (and multi) Reggeon vertex due to the B-field only affect the zero modes and can be written in a simple and elegant way. Therefore we can easily sew these vertices together and write the general expression for the multiloop N-Reggeon vertex, which contains any loop string amplitude, in presence of the B-field. The field theory limit is also considered in some examples at two loops and reproduces exactly the results of a noncommutative scalar field theory.

Latex. 27 pages. 9 figures v2: typos corrected, references added; v3: ref. added, version to appear in NPB

References in corpus (5)

• String Theory and Noncommutative Geometry
• Non-commutative World-volume Geometries: Branes on SU(2) and Fuzzy Spheres
• Constrained Quantization of Open String in Background B Field and Noncommutative D-brane
• Manifest Supersymmetry in Non-Commutative Geometry
• Two-Loop ${\varphi }^4$-Diagrams from String Theory

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• Space-Time Noncommutative Field Theories And Unitarity
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• The noncommutative harmonic oscillator in more than one dimensions
• Noncommutative D-brane and Open String in pp-wave Background with B-field
• Hermitian Analyticity, IR/UV Mixing and Unitarity of Noncommutative Field Theories
• Noncommutative $\mathcal{N}=1,2$ super U(N) Yang-Mills: UV/IR mixing and effective action results at one loop
• Excitations in Hot Non-Commutative Theories
• The twisted open string partition function and Yukawa couplings
• Wrapped Magnetized Branes: Two Alternative Descriptions?
• Effective String Tension and Renormalizability: String Theory in a Noncommutative Space
• Non-commutative (D)-instantons
• D1-Strings in Large RR 3-Form Flux, Quantum Nambu Geometry and M5-Branes in C-Field
• Factorization and generalized *-products
• One-loop Noncommutative U(1) Gauge Theory from Bosonic Worldline Approach
• Open Wilson Lines as States of Closed String
• Noncommutativity from the string perspective: modification of gravity at a mm without mm sized extra dimensions
• Anatomy of Two-Loop Effective Action in Noncommutative Field Theories
• Cutting rules and perturbative unitarity of noncommutative electric-type field theories from string theory
• Systematics of one-loop Yang-Mills diagrams from bosonic string amplitudes
• Unitarity of noncommutative field theories from string theory
• Stretched strings and worldsheets with a handle
• Transplanckian Dispersion Relation and Entanglement Entropy of Blackhole
• Open string derivation of winding states in thermal noncommutative field theories
• Multiloop Noncommutative Open String Theory and their QFT limit
• Non-Commutative Gauge Theories and the Cosmological Constant
• One-loop unitarity of string theories in a constant external background and their Seiberg-Witten limit