Introduction to conformal field theory, Lecture 1

In this seminar I will, over some 10 lectures, introduce the basics of conformal field theory. The emphasis will be on the physical content, however, there will be reference to mathematical formulations throughout.

The course is based on a mixture of Ginsparg's "Applied Conformal Field Theory", hep-th/9108028 and Schottenloher's "A mathematical introduction to conformal field theory".

Prerequisites for the course comprise: advanced QM, QFT, advanced QFT, and some familiarity with symplectic methods, which you can cover by watching my previous videos.

In the first lecture I introduce the conformal group, and its classification via infinitesimal actions.

[annahua]

Dear Prof. your lectures in CFT is extremely helpful for students. I had a lot of trouble when I learned CFT by myself. Thank you so much for sharing your videos.

[jonahchan]

Do really thanks for giving such a nice precious comprehensive resource, the videos, which means a lot for the students like me.

[abhisheknavhal]

@18:33, 24:07, 30:28, 39:08, 43:55, 47:15, 53:16, 58:32, 1:01:56, 1:07:26, 1:14:05 oddly satisfying! Amazing lecture.

[a.s.]

Excellent! Feeling very at-home with the language and setup, especially after going through QFT and Advanced QFT.

[KRO]

Great video, I like how you try to give a flavor of what is to come in the next lectures, and I think more teachers should do the same.

[redrum]

Great lecture. Very accessible and concise.

[stervi]

Dear Tobias, why do we say that a theory has conformal symmetry if there exists a unitary representation of the conformal group? Surely the fact that we have a unitary representation isn't telling us anything about the physical states of the system. For example, we can define a unitary representation of the group of translations by exponentiating the momentum operator whether our system has translational symmetry or not, i.e. whether translations commute with the Hamiltonian or not. Thank you

[khoanguyen]

How are CFT and effective field theory (EFT) related? CFT is an infrared limit of QFT, and EFT obtains from QFT by integrating out the ultraviolet scale. So, CFT is EFT in this case?
I also see people discuss about relevant operator in both CFT and EFT

[jackstacks]

This series is very well done, thank you.

[杨晓晗]

Thanks for sharing the excellent lecture! But I have a small question. At about 41:30 when you write down the infinitesimal transformation of the metric, should it be g_{\mu\nu} - (\partial_\mu \epsilon_\nu + \partial_\nu\epsilon_\mu)? I just mean may be the sign should be minus but not plus since we take \frac{\partial x}{\partial x^\prime}. Thanks a lot ！: )

[janmajaykumar]

Wonderful Lecture .. I watched just first lecture. I request please have a lecture series on Chern Simons theory

[yuzhiliu]

So why the conformal symmetry is show near only the critical point, not order phase or disorder phase?

[relikep]

I don't understand a point:
when you take trace of \eta_{\mu\nu} why isn't the answer p-q but p+q=d?

[hongyao]

Hi, should denominator of the angle be \sqrt{g_\mu\nu u^\mu u^\nu * g_\mu\nu v^\mu v^\nu }?

[evalsoftserver]

DdDark energy  exsist  as a FIELD INVARIANCE of Space configuration "PHASALITY"  using a form of Spatial automorphism to auto regulate  (gauge) ( ENGAGE)  or Break Symmetry, the amount of energy,   time, Velocity ( NEWTONIAN MECHANICS)  plus {frequency), and Volume   required to Continuous Transform  Any particle matter of that  SPACE TIME "Configuration" ( FIELD,   TENSOR, PARTICLE WAVE ENERGY PAIRING ) (LANGRAININ MECHANIC ) at that specific location, ` or at any future location  in that Space Time, Ex. photons or light like particles Traveling  in a straight line at a Fraction  of speed of light (ECLUDIEAN SPACETIME DILATION) gives rise to Baryonic mass  and (RADIOACTIVE DECAY ) through Quasi-Local Fields INTERACTION SCALAR FIELD  "PHASING"  like (HIGGS BOSON)  particles fields, Extending into like matter electron proton ect. thru When ( Riemann space)  gravity, electromagnetic, nuclear Strong force is engaged thru Baryionic Field Boson interaction    the electromagnetic Photon Particle enters  and engages Curvatured Space. Reaching infinite mass (NEAR INFINITE PHASALITY) for that particle wave location causing a curved Deceleration  we call gravity.and Electromagnetism 


Entanglement  happens  by Shears  TRANSFORMATION of this Baryonic mass/particle/ when Space  itself shears and Rotates, Like a Automorphism mapping of Space, So all FIELD in that  Space becomes INVARIANT Orients itself, to a common point  enabling one PARTICLES  (like the MUON) to exist as a COLLAPSING  Wave Function in Two Different Non-Local SPACES or fields. (PHASE) or thru a local Field SYMMETRY, and Because Information travels in a Linear fashion in 3 Dimension Space, We olny become Aware of this Spacetime Information by attempting to Communicate   outside  our everyday 4 Dimensional  Spacetime . and Not Seeing, or Receiving anything  back then we say mass is missing,  


Entangled particles  don't need this  Same Time information to Communicate 

because it Exists at every point in the Entangled PARTICLES BARYONIC MASS WAVE function . The SpaceTime Coordinates has Shared Merging at a Every Point  in the field .So Field  Entaganelment is   (BOTH)a Attractive Force Within a mutual, Baryonic LEPTON MUON MESON  Field space is a Repulsive Force where the Wave Particle are  Running Away from Itself as  a non local non mutual (RELATIVISTIC )field, So when you observe or try to measure the Particle the Wave function does not Collapses because the wave and Particle exsist as non mutual independent Quasi local  Field OVER A DISTANCE WAVE  or a Gauge less field for Relativistic and Quantum Field Entanglement the Field Symmetry  Collapse of breaks from a ( DIALATED SCALAR Field




So Dark Matter Could be a Non-Localized Spacetime like a Black Hole with Equally distributed gravitational mass and inertial mass .Analysis of high velocity Nuetrino burst from Gamma  rays as Observed from our 4 Dimensional Spacetime Frame of Reference might confirm this. Were the Nuetrino ACT as a SYMMETRY break of ENTROPY (Gauge Field) breaks and lose its Orientation.and  this ROTATIONAL SYMMETRY break can be Non-Local  or Quasi-Local Field when all Particle waves FIELD and SPACES becomes INVARIANT UNDER A mutual FLAT MANIFOLD