String fields, higher spins, and number theory

Includes bibliography (p. 193-197) and references

1.Introduction: Massive Higher-Spin Modes in String Dynamics and Tensionless Limit 1.1.String Theory and Higher-Spin Dynamics 1.2.Massive Higher Spin Modes in Bosonic String Theory: A Brief Review 2.Geometry of Superconformal Moduli in Superstring Theory 2.1.Bosonic and Fermionic Ghost Pictures in String Amplitudes 2.2.Ghost-Matter Mixing and Moduli Space Singularities 3.Higher Spin Dynamics in a Larger String Theory 3.1.Ghost Cohomologies and Hidden Space-Time Symmetries in String Theory 3.2.AdS Isometries in Superstring Theory 3.3.Vertex Operators for Frame-Like Higher-Spin Fields and AdS Higher-Spin Algebra 4.Interactions of Higher Spin Fields in Larger String Theory 4.1.Vertex Operators in the Frame-Like Formalism 4.2.Vertex Operators for Symmetric Higher-Spin Frame-Like Fields: The Spin 3 Case 4.3.Higher Spins Operators, Weyl Invariance and Emergence of AdS Geometry Contents note continued: 4.4.Higher Spin Operators: Weyl Invariance and β-Functions 4.5.3-Point Amplitude and 3-Derivative Vertex 4.6.Quartic Interactions and Nonlocalities 4.7.A Glance at Quintics 4.8.Quintic Interactions and Localization 4.9.Reading off the Quintic Vertex 5.Bosonic Strings, Background Independence and Analytic Solutions 5.1.Background Independence - Some Preliminaries 5.2.Analytic String Field Theory Solution for AdS3 Vacuum 5.3.Structure Constants, Higher Spins and SFT Solutions: A Warm-Up Example 5.4.CFT Properties of SFT Ansatz 5.5.Bell Polynomial Operators: Operator Products and Correlators 6.Higher Spins as Rolling Tachyons in Open String Field Theory 6.1.Irregular Vertex Operators as Holographic Duals for Mixed-Symmetry Higher Spins 6.2.Irregular Vertices as String Field Theory Solutions: Rank 1 Case 7.An Analytic Formula for Numbers of Restricted Partitions from Conformal Field Theory Contents note continued: 7.1.Generating Function for Partitions: The Correlator 7.2.Partition-Counting Correlator: The Conformal Transformations 7.3.Tests and Comments.

The book aims to analyze and explore deep and profound relations between string field theory, higher spin gauge theories and holography--the disciplines that have been on the cutting edge of theoretical high energy physics and other fields. These intriguing relations and connections involve some profound ideas in number theory, which appear to be part of a unifying language to describe these connections.