conformal bootstrap lecture notes
| ArXiv:160207982v1 [hep-th] 25 Feb 2016 methods focusing on |
| ArXiv:160207982v1 [hep-th] 25 Feb 2016 |
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Notes on the Conformal Bootstrap
Notes on the Conformal Bootstrap These notes are an addendum to my 2008 les Houches lecture notes For further details see eg http://arxiv org/ pdf /1111 2115 pdf Global conformal invariance for any d constrains the 4-point function of the same (scalar) eld to have the form 2 2 x 34 C = h (x1) (x2) (x3) (x4)i = x 12 g(u; v) |
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Weizmann Lectures on the Numerical Conformal Bootstrap arXiv
tended to familiarize students with the nuts and bolts of the numerical bootstrap as e ciently as possible After a brief review of the basics of conformal eld theory in d>2 spacetime dimensions we discuss how to compute conformal blocks formulate the crossing equations |
Are conformal bootstrap 29 constructions inverse to each other?
TASI Lectures on the Conformal Bootstrap 29 constructions above are inverse to each other, with the identification O(0) !O (0)|0i⌘|O.i (83) This is the “state-operator correspondence.” It is straightforward to see how the conformal group acts on states in radial quantization.
What are the unitarity bounds of a conformal bootstrap?
TASI Lectures on the Conformal Bootstrap 39 In summary, we have the unitarity bounds = 0 (unit operator), or 2 ( d2` =0, `+d2 `>0. (130) 7.3.1. Null States and Conserved Currents Ifsaturates the bounds (130), the conformal multiplet will have a null state. For the unit operator, all descendants are null.
What's new in TASI lectures on conformal bootstrap 9?
TASI Lectures on the Conformal Bootstrap 9 new operators on this new Hilbert space would be unchanged. For exam- ple, if we arrange the operators as shown on the right-hand side of (11), we always get the correlator on the left-hand side.
What is a good book about bootstrap?
arXiv:1504.07997. R. Yacoby, Accidental Symmetries and the Conformal Bootstrap (2015). arXiv:1507.04424. L. Iliesiu, F. Kos, D. Poland, S. S. Pufu, D. Simmons-Du n, and R. Yacoby, Bootstrapping 3D Fermions (2015). arXiv:1508.00012.
2. QFT Basics
The rst step of the conformal bootstrap is to determine the full conse-quences of symmetries. In this section, we quickly review symmetries in quantum eld theory, phrasing the discussion in language that will be use-ful later. We work in Euclidean signature throughout. arxiv.org
[P ; O(x)] = @ O(x); (15)
without specifying a quantization. In fact, from now on, we will no longer distinguish between path integral insertions O(x) and quantum operators bO(x). The expression [Q; O(x)] can be interpreted as either an actual commutator [ Q; b bO(x)] in any quantization of the theory, or in path-integral language as surrounding O(x) with a topological surf
3. Conformal Symmetry
In a conformal theory, the stress tensor satis es an additional condition: it is traceless, arxiv.org
Exercise 3.2. Show that k
= Ip I. k Conclude that ea implements the transformation arxiv.org
3.2. The Conformal Algebra
The charges Q give a representation of the conformal algebra [Q arxiv.org
4. Primaries and Descendants
Now that we have our conserved charges, we can classify operators into representations of those charges. We do this in steps. First we classify op-erators into Poincare representations, then scale+Poincare representations, and nally conformal representations. arxiv.org
4.1. Poincare Representations
In a rotationally-invariant QFT, local operators at the origin transform in irreducible representations of the rotation group SO(d), arxiv.org
4.2. Scale+Poincare Representations
In a scale-invariant theory, it's also natural to diagonalize the dilatation operator acting on operators at the origin, arxiv.org
: : : KnO(0)
with arbitrarily low dimension. Because dimensions are bounded from below in physically sensible theories, this process must even-tually terminate. That is, there must exist operators such that arxiv.org
x 7 g1(g2(x)), and Ug is the unitary operator associated to g1g2 denotes composition
g. full conformal group. It is also called a parabolic Verma module. Sometimes the operator satis es \\shortening conditions" where a linear combination of descendants vanishes. conserved current is an example.) In this case, the Verma module is reducible and the actual conformal multiplet of O is one of the irreducible components. arxiv.org
On( xn)i; (82)
with su ciently large to de ne the correlator. Since the xi can now be arbitrarily close together, we have de ned local operators.u arxiv.org
OE(tE; x) ix HtE+ix OL( itE; x) = eHtE PLOL(0; 0)e PL: (96)
of O(x) and the at-space calculation applies. This de nition might not be consistent with other independent de nitions. For instance, if O(x) is the stress tensor, it gives a di erent answer from the canonical de nition (8) because of the Weyl anomaly. zWe make some brief comments about Euclidean vs. Lorentzian eld theory and analytic continuation
j i = O( tE1) O( tEn)j0i: (103)
For brevity, we suppress the spatial positions of the operators. The conju-gate state is given by That is, h j arxiv.org
8.1. Consistency with Conformal Invariance
Conformal invariance strongly restricts the form of the OPE. For simplicity, suppose Oi, Oj, and Ok are scalars. arxiv.org
h (x1) (x2) (x3) (x4)i = h0jRf (x3) (x4)gRf (x1) (x2)gj0i: (154)
For a primary operator O, let jOj be the projector onto the conformal multiplet of O, arxiv.org
X jOj (155) ; j iN 1h j; N h j i:
=O;PO;PPO;::: The identity is the sum of these projectors over all primary operators. arxiv.org
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TASI Lectures on the Conformal Bootstrap
25 févr. 2016 These notes are from courses given at TASI and the Advanced Strings. School in summer 2015. Starting from principles of quantum field theory. |
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1 Exercise: Conformal Algebra
The basic lecture notes are. • S. Rychkov “EPFL Lectures on Conformal Field Theory in d ? 3 Dimensions |
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Conformal Blocks: notes references and exercises 1. Introduction 2
A nice of lecture notes on CFT in d > 2: TASI Lectures on the Conformal Bootstrap ... EPFL Lectures on Conformal Field Theory in D ? 3 Dimensions. |
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Lectures on Conformal Field Theories
21 oct. 2019 The subject of CFTs in four and later three |
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Introduction to two-dimensional conformal field theory
This allows us to define and solve minimal models and Liouville theory. We also introduce the free boson with its abelian affine Lie algebra. Lecture notes for |
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Introduction to Conformal Field Theory Trinity Term 2014 Prof. J
Trinity Term 2014. Prof. J. Cardy. Notes on the Conformal Bootstrap. These notes are an addendum to my 2008 les Houches lecture notes. For further details. |
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Weizmann Lectures on the Numerical Conformal Bootstrap
1These lecture notes are heavily based on the previous lecture notes [12] |
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A Mellin Space Approach to the Conformal Bootstrap arXiv
25 nov. 2016 The conformal bootstrap is the philosophy that these constraints are strong ... We note that since each Witten exchange diagram contains the. |
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Lectures on AdS/CFT from the Bottom Up
Abstract. AdS/CFT from the perspective of Effective Field Theory and the Conformal Bootstrap. 1.4 Brief Notes on the History of Holography . |
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Conformal field theory for particle physicists arXiv:2207.09474v2
8 août 2022 This is a set of introductory lecture notes on conformal field theory. Unlike most existing reviews on the subject CFT is presented here ... |
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Notes on the Conformal Bootstrap
Introduction to Conformal Field Theory Trinity Term 2014 Prof Conformal Bootstrap These notes are an addendum to my 2008 les Houches lecture notes |
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1 Exercise: Conformal Algebra - CERN Indico
The basic lecture notes are • S Rychkov, “EPFL Lectures on Conformal Field Theory in d ≥ 3 Dimensions,” [1] • D Simmons-Duffin, “The Conformal Bootstrap ,” |
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Lectures on the Conformal Bootstrap 1 Introduction - ICTS
11 jui 2015 · Note that g has mass-dimension 1, so that perturbation theory leads to an expansion in xg, where x is a distance scale At distances x ≫ 1/g, this |
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Lecture notes
We introduce conformal field theory in two dimensions, from the basic principles to some of the simplest models From the representations of the Virasoro algebra |
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EPFL Lectures on Conformal Field Theory in D≥3 Dimensions
Many thanks to Georgios Karananas who took notes and typed them back in Qualls, J D : Lectures on conformal field theory, arXiv:1511 04074[hep-th] xii |
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Solving Conformal Theories with the Bootstrap - Overview and
28 juil 2015 · Method is conformal bootstrap and will be focus of these lectures 9 ( incomplete) References ▻ Slava Rychkov's d > 2 CFT lecture notes: |
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Lessons for conformal field theories from bootstrap and holography
analyzed the analytical aspects of the Conformal Bootstrap program to gain [1] R Gopakumar,“Lecture notes on Holographic AdS/CFT Correspondence, 2013 |
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Lectures on Conformal Field Theories - Department of Applied
21 oct 2019 · and the resurgence of the conformal bootstrap as surprisingly accurate Although perhaps pedestrian these lectures are not intended Using the expression for the energy momentum tensor in (4 35) (it is useful to note that |
