Tuesday, July 11, 09:30 - 10:00 Opening











G. Arutyunov

lecture 1


C. Grojean

lecture 2


C. Grojean

lecture 3


Seminar 1


G. Arutyunov

lecture 4


C. Grojean

lecture 5


C. Grojean

lecture 6


Seminar 2


G. Arutyunov

lecture 7


C. Grojean

lecture 8


I. Volobuev

lecture 9


Seminar 3


G. Arutyunov

lecture 10


I. Volobuev

lecture 11


K. Melnikov

lecture 12


Seminar 4


G. Arutyunov

lecture 13


I. Volobuev

lecture 14


K. Melnikov

lecture 15


Seminar 5








Evening party


K. Melnikov

lecture 16


D. Gorbunov

lecture 17


I. Volobuev

lecture 18


Seminar 6



K. Melnikov

lecture 19


D. Gorbunov

lecture 20


G. Arutyunov

lecture 21


Seminar 7


K. Melnikov

lecture 22


D. Gorbunov

lecture 23


Selected talks by participants


Concert of string quartet


D. Gorbunov

lecture 24


D. Gorbunov

lecture 25


I. Volobuev

lecture 26


Seminar 9

Thursday, July 20,  Closing


There should be a 5-10 minutes break in the middle of each lecture

Seminars are devoted to problem solving and informal discussions. Each seminar is associated to one or another lecture course

G. Arutyunov lectures outline:

1. Fields and symmetries

2. Quantization

3. Scattering theory

4. Renormalization

5. Non-abelian gauge theories

6. Resurgence (if time permits)


Recommended literature:

[1] M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory, Perseus Books, The Advanced Book Program (Reading, MA). (русский перевод: М.Пескин, Д.Шредер. Введение в квантовую теорию поля. Пер. с англ. R&C, Москва, Ижевск. 2001)

[2] L. Faddeev and A. Slavnov, Gauge Fields: An Introduction to Quantum Theory, Westview Press. (А. А. Славнов, Л. Д. Фаддеев, Введение в квантовую теорию калибровочных полей, Наука, М., 1978 , 240 с)

[3] P. Ramond, Field Theory: a Modern Primer, Addison Wesley. (П . Рамон ТЕОРИЯ ПОЛЯ . СОВРЕМЕННЫЙ ВВОДНЫЙ КУРС М . : Мир, 1984, 336 с)

[4] D. Dorigoni, An Introduction to Resurgence, Trans-Series and Alien Calculus, arXiv:1411.3585 [hep-th].

I. Volobuev lectures outline:

Lecture 1: A historical introduction: scalar gravity theories and the theory of general relativity. Introduction to general relativity. The equivalence principle. Chronogeometry. Curvilinear coordinates. Distances and time intervals. Galilean coordinates. Linear connection and covariant differentiation. Riemannian connection. Lagrangian and equations of motion for the gravitational field. Linearized theory.

Lecture 2: Kaluza-Klein theories. Isolation of the physical degrees of freedom. Dimensional reduction of the zero mode sector. The problem of electric charge.

Lecture 3: Spontaneous compactification. The choice of matter fields. Symmetric gauge fields. Equations of spontaneous compactification with symmetric gauge fields. Dimensional reduction and model building.

Lecture 4: Large extra dimensions. Rubakov-Shaposhnikov example. ADD scenario. Randall-Sundrum model. The RS solution and its physical interpretation. The radion and the necessity of stabilization.

Lecture 5: Phenomenology of the stabilized Randall-Sundrum model. Processes with Kaluza-Klein gravitons. Higgs-radion mixing and searches for the radion dominated state. Universal extra dimensions and processes with Kaluza-Klein excitations of the SM gauge bosons.

Problem 1: Second variation Lagrangian and the linearized equations of motion of the gravitational field in an arbitrary background.

Problem 2: Wave functions in the extra dimension for Kaluza-Klein modes of gravitational, scalar, vector and spinor fields in the unstabilized Randall-Sundrum model.


Recommended literature:

[1] Л.Д. Ландау, Е.М. Лифшиц. т. 2, Теория поля. Наука 1988.

[2] А. Ходос. Теории Калуцы-Клейна: общий обзор УФН 146 647–654 (1985)

[3] И.П. Волобуев, Ж.М. Моурао, Ю.А. Кубышин, Г. Рудольф. Размерная редукция симметричных калибровочных полей, модели Хиггса и спонтанная компактификация. ЭЧАЯ т. 20, N3, 561-627, 1989.

[4] E.E. Boos, Y.A.Kubyshin, M.N. Smolyakov and I.P. Volobuev, Effective Lagrangians for physical degrees of freedom in the Randall- Sundrum model, Class. Quant. Grav. 19 (2002) 4591

[5] Э.Э. Боос, В.Е. Буничев, И.П. Волобуев, М.Н. Смоляков, Геометрия, физика и феноменология модели Рэндалл-Сундрума. ЭЧАЯ т. 43(1), стр. 82-155, 2012.


K. Melnikov lectures outline:

1) perturbative SM computations and the LHC physics program

2) modern methods for tree-level computations (spinor helicity, color ordering, BCFW recursion).

3) one-loop computations in the generalized unitarity framework

4) modern techniques for two-loop computations

5) subtraction techniques at NLO and NNLO


1) four-gluon scattering amplitudes in spinor-helicity formalism.

2) N-gluon MHV amplitudes from BCFW recursion

3) HIggs decay to two photons through a loop of nearly massless scalars in the generalized unitarity framework

4) soft and collinear limits of QCD scattering amplitudes


Recommended literature:

[1] M. Peskin ``Simplifying multi-jet QCD computations'' : arXiv:1101.2414

[2] R. K. Ellis et al. `` One-loop computations in Quantum Field Theory: from Feynman diagrams to unitarity cuts'' : arXiv:1105.4319

[3] J. M. Henn ``Lectures on differential equations for Feynamn integrals'', arXiv:1412.2296

[4] F, Caola et al. ``Nested soft-collinear subtractions in NNLO QCD computations'', arXiv:1702.01352


C. Grojean lectures outline:

Lecture 1: Dimensional analysis, EW theory and SM Higgs mechanism

0. Particle physics and dimensional analysis: natural units vs hbar dimension

1. Beta decay & Fermi theory

2. SU(2)xU(1) vs Georgi-Glashow

3. pi -> e barnu_e vs pi -> mu barnu_mu and V-A structure of the weak interaction

4. SM Higgs mechanism - W and Z masses

5. SU(2)xU(1)->U(1)em, number of degrees of freedom before and after EWSB

6. rho parameter

7. custodial symmetry 




W_L and Z_L as pions of SU(2)xSU(2)/SU(2), Sigma matrix, unitary gauge

ex 1: more on hbar dimensions: 2->2 processes, 2-> n processes, interaction scale vs mass scale

ex 2: how many particles in the SM? -> anomaly cancelation


Lecture 2: Goldstone equivalence theorem, WW scattering, Higgs unitarization

1. h->WW - computation in the unitary gauge and using the Goldstone's (using the Higgs potential)

2. t -> Wb - computation in the unitary gauge and using the Goldstone's (using the Yukawa interaction)

3. validity of the Goldstone eq. theorem: m << E << 8 pi m/g

4. expression of longitudinal polarization vector and eps_L (k) ~ k/mW (1+ O(m_W^2/E^2))

5. WW scattering in the unitary gauge: cancelation of the E^4 terms

6. Higgs unitarization for WW->WW, WW->hh, WW-> ff

7. Short discussion on the Higgs production channels at the LHC

8. Remark on the importance of h->gg and h->gam gam as test of naturalness H->gg top quark loop: diagrammatic computation and mt->infinity limit, remark on apparent (non-)decoupling,

ex 3: Higgs self-couplings, general expression of the rho parameter

ex 4: partial wave decomposition


Lecture 3: RG effects in Higgs potential, hierarchy problem

1. triviality bound

2. stability bound

3. general discussion on the problem of quadratic divergences, relevant operators.

4. computation of the quadratically divergent diagrams

5. Coleman-Weinberg potential

6. solutions to the hierarchy problem: susy vs composite

ex 5: quadratic divergence from Coleman-Weinberg potential

ex 6: Higgs potential in composite models: (v/f)^2 tuning


Lecture 4: Higgs&BSM: effective theory approach

1. Higgs couplings modifications due to the (d_mu H^2)^2 operator

2. Universality of Higgs coupling deviations close to SM

3. Higgs primary operators

4. SILH basis and power counting (hbar dimensions again)

5. SO(5)/SO(4) composite Higgs models. Matching with EFT

6. Flat direction: top Yukawa - contact interactions to gluons/photons Higgs+jet boosted channel off-shell channel

ex 7: computation of S and T from dim. 6 operators

ex 8: non-linear field redefinition in presence of the (d_mu H^2)^2 operator.


Lecture 5: BSM varia

0. GUT

1. Extra dimensions: large vs warped

2. Symmetry breaking by boundary conditions

3. AdS/CFT model building for phenomenology: Higgsless and composite Higgs

4. Higgs-cosmology interplay: relaxion model to solve the hierarchy problem

ex 9: beta function (SM and MSSM, also for SUSY N=2, 4), conditions for unification

ex 10: AdS5 and Randall Sundrum model


Extra material (if time permits or if there is strong interest):

1. Finite temperature corrections, EW phase transition in the SM vc/Tc = 4 B v^2/ mh^2 with B= (2 mW^3+ mZ^3)/(6 pi v^3)~ 6 10^-3

2. Hgg and Hgamgam effective vertex: matching with diagrammatic computation

3. HLET from alpha_s and alpha_em runnings

4. Non-interference theorem: SM - BSM

5. Higgs portal models: power counting


D. Gorbunov lectures outline:

1. Introduction: physical components, major observables and basic description.

2. BBN and recombination

3. Inflation and reheating

4. Baryogenesis and Dark Matter

5. Miscellaneous: modified gravity, fuzzy dark matter, galileons, etc