2005 Summer Institute on String Summer School on String R833, New Physics Building National Taiwan University I will start with a basic introduction to D-brane and explaining how noncommutative geometry arises in string theory. Then we will explore the properties of noncommutative field theory. The emphasis will be on the novel aspects in contrast to the usual local quantum field theory. Applications of noncommutative geometry to other areas such as tachyon condensation and AdS/CFT will be discussed. Introduction to noncommutative geometry in string and field theory Chong-Sun Chu (Durham) 7/25 ( Mom )7/26 ( Tue )7/27 ( Wed )7/28 ( Thur )7/29 ( Fri ) 09: :00Taylor 1/4Taylor 3/4Russo 1/4Hashimoto 1/3Mathur 2/3 10: :10Taylor 2/4Taylor 4/4Russo 2/4Hashimoto 2/3Mathur 3/3 11: :30Liu 1/4Liu 3/4SeminarMathur 1/3Hashimoto 3/3 Lunch 14: :10Liu 2/4Liu 4/4Russo 3/4Seminar 15: :30Chu 1/4Chu 3/4Russo 4/4Seminar 16: :40Chu 2/4Chu 4/4Seminar Banquet Program Topic and Speakers In these lectures, I will review Liouville theory as string theory in non-critical dimensions, matrix model formulations of these string theories, and recent developments in supersymmetric non-critical string theories and D-branes. Topics will include ground ring relations, large N techniques, integrability, FZZT and ZZ branes, open/closed string duality, and topological gravity. Introduction to matrix model and non-critical string theory Akikazu Hashimoto (Wisconsin) Exact solutions in supergravity theory James Liu (Michigan) I will begin with an introduction to supergravity, focusing on theories in 10 and 11 dimensions, which are closely connected to string theory. Of particular interest are supergravity configurations preserving some fraction of supersymmetry. These include typical string backgrounds such as Calabi-Yau spaces as well as gravitational objects such as supergravity p-branes and BPS black holes. I will discuss the construction and classification of such BPS solutions, focusing especially on the analysis of the Killing spinor equations and holonomy in supergravity. ＊ The purpose of the school is to introduce recent developments in string theory to beginners. 25 ~ 29 July

2005 Summer Institute on String Summer School on String R833, New Physics Building National Taiwan University We begin with an overview (no technical details) of the current status of string theory: perturbative string theories, dualities, D-branes,M-theory and nonperturbative formulations of string theory. D- branes are then described in more detail from the points of view of 10D supergravity and perturbative string theory. Fluxes on D-branes are introduced and used to show how D-branes of one dimension can describe D-branes of another dimension.Finally, fluxes in supergravity are introduced and used to stabilize moduli of string compactifications. Branes and fluxes in string theory and M-theory Washington Taylor (MIT) Intersecting branes Rodolfo Russo (CERN) D-branes provide a natural framework for realizing in string theory two main building blocks of the Standard model: non-abelian gauge symmetries and chiral fermions. We start by showing how these features arise naturally in configurations with intersecting D-branes (or, in the T-dual language, D- branes with fluxes). Then we discuss tree-level (disk) string amplitudes and show how to derive the low energy effective action from string computations. Finally we will discuss some possible phenomenological applications of this string constructions. Topic and Speakers (cont.) Sponsors: Sponsors: National Center for Theoretical Sciences ( NCTS ) Asia Pacific Center for Theoretical Physics (APCTP) Center for Theoretical Physics (NTU) Organizers: Organizers: Chuan-Tsung Chan (NCTS) Chiang-Mei Chen (National Central University) Wenfeng Chen (NCTS) Ting-Wai Chiu (National Taiwan University) Chong-Sun Chu (Durham University) Xiao-Gang He (National Taiwan University) Pei-Ming Ho (National Taiwan University) Hsien-Chung Kao (National Taiwan Normal University) Yeong-Chuan Kao (National Taiwan University) Jen-Chi Lee (National Chiao-Tung University) Feng-Li Lin (National Taiwan Normal University) Correspondence ： Ms. Chia-Chi Liu Tel: Fax: ＊ 25 ~ 29 July We will start by understanding Hawking radiation from black holes, and why this creates a conflict with quantum mechanics. We will review how string theory leads to an understanding of black hole entropy. We will then ask: What is the internal structure of a black hole? We will construct the microstates for 2-charge black holes, and also see how some microstates for 3-charge holes can be constructed. We will try to extend the lessons learnt here to conjecture how generic black holes would behave like `fuzzballs' where the entire region inside the `horizon' is nontrivial and carries the information of the black hole state. The black hole information paradox Samir Mathur (Ohio State)