**Record:** Yes

**Level:** Graduate

**Language:** English

**Prerequisite**

Basic mathematics (calculus, algebra, etc.); a textbook knowledge of General Relativity and Quantum Field Theory (including the very basics facts about supersymmetry); the elementary notions of differential geometry (Riemannian geometry, bundles, connections, etc.), Lie groups, and algebraic topology (homology & cohomology groups,etc.).

**Abstract**

A comprehsive course in String Theory.

String Theory I covers the foundations of the theory, the construction of the various string theories, with emphasis on the supersymmetric ones, and the basic computational techniques. The emphasis is on SUSY string theories, the bosonic string is used mainly as a didactical laboratory where we introduce basic ideas and techniques in the simplest possible context. While the approach is meant to be didactical, one tries to be mathematically precise, and self-contained. Conformal field theory in two-dimensions is introduced from scratch, with the topics relevant to string theory discussed in detail.

String Theory II covers the physics of the supersymmetric strings, from the perturbative regime to the non-perturbative one. The theory of supergravity and anomalies are reviewed from a geometric perspective. BPS objects and non-renormalization theorems are described from different viewpoints. Calabi-Yau compactifications are discussed in detail. The course covers also some advanced stuff such as the basic ideas of M- and F-theory, black hole entropy, and so on.

**Reference**

Sergio Cecotti, Introduction to String Theory, Springer, to be published (spring 2023). String I covers chapters 1-7 of the book, String II covers chapters 8-14. The book contains an extensive bibliography to books, reviews, and original literature.

**Syllabus**

Introducing Strings: the Polyakov Path Integral

– Introduction

– Bosonic String: the Polyakov Action

– Bosonic String: Light Cone Quantization

– Covariant Quantization á la Polyakov

– The Weyl Anomaly

– Ghost Zero-Modes: Aut(Σ) and WP Moduli Geometry

– The Superstring

– Strings Moving in Curved Background

– Physical Amplitudes, S-Matrix, and Vertices

Two-dimensional Conformal Field Theories

– Space-Time Symmetries in QFT

– Conformal Field Theory (CFT)

– CFT in Two-Dimension

– The 2d Free Massless Scalar

– Free CFTs and their Bosonization

– Inclusion of Boundaries. Non-orientable Surfaces

– Kac-Moody and Current Algebras

– (1; 1) Superconformal Algebra

– SO(2n) Current Algebra at Level 1 and Lattices

– Classification of 2d Superconformal Algebras

Spectrum, Vertices,and BRST Quantization

– The Superstring Lorentz Current Algebra

– The Physical Spectrum: Light-Cone Gauge

– Old Covariant Quantization

– OCQ: Physical Conditions vs. 2d Superfields

– BRST Invariance: Generalities

– BRST Quantization of the Bosonic String

– BRST Quantization of the Superstring

– Space-TimeSupersymmetry

– Open Strings: Chan-Paton Degrees of Freedom

Bosonic String Amplitudes

– Path Integrals for Non-Compact

– Amplitudes for the b,c CFT

– The Veneziano Amplitude

– Chan-Paton Labels and Gauge Interactions

– Closed StringTree-Level Amplitudes

– One-Loop Amplitudes: the Torus

– One-Loop: the Cylinder

– Boundary and Crosscap States

– One-Loop: Klein Bottle and MöbiusStrip

Consistent Ten-Dimensional Superstring Theories

– Two-Dimensional Global Gravitational Anomalies

– Consistent Closed Superstring Theories in 10 Dimensions

– Consistent Unoriented and Open Superstrings

– Two-Dimensional Fermionic Path Integrals

– Modular Invariance in TypeII

– Divergences and Tadpoles in TypeI Theories

Bosonic String: T-Duality & D-Branes

– Toroidal Compactifications in Field Theory

– 2d CFT of a Compact Scalar

– T-Duality in Closed Strings

– Narain Compactifications

– Abelian Orbifolds

– Open Strings: Wilson Lines

– Open Bosonic String: T-Duality

– D-Branes (in Bosonic Strings)

– T-Duality of Unoriented Strings: Orientifolds

The Heterotic String

– Constructing String Models

– The SO(32) and E_8 × E_8 Heterotic Strings in 10d

– Non-Supersymmetric Heterotic Strings in 10d

– Heterotic Strings: the Bosonic Construction

– Classification of Even Self-Dual Lattices

– SUSY Heterotic Strings in d=10(Bosonic Form)

– Toroidal Compactifications

– Supersymmetry and BPS States

**Lecturer Intro**

Sergio Cecotti graduated in physics at the University of Pisa in 1979 and has worked at the Harvard University, the University of Pisa, CERN, etc.. In 2014, he became a full professor at SISSA. He has published about 100 papers with total number of citations 7260. His h-index is 44.

**Lecturer Email:** cecotti@sissa.it

**TA:** Dr. Yiyu Lin, yiyu@bimsa.cn