Modulated Vacua - Agenda (Indico) · Muneto Nitta (Keio U.) Modulated Vacua Topological Solitons,...
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Muneto Nitta (Keio U.) Modulated Vacua Topological Solitons, Nonperturbative Gauge Dynamics and Confinement 20-21 July 2017, University of Pisa arXiv:1706.02938 [hep-th], arXiv:1706.05232 [hep-th] with Shin Sasaki (Kitasato) & Ryo Yokokura (Keio)
Transcript of Modulated Vacua - Agenda (Indico) · Muneto Nitta (Keio U.) Modulated Vacua Topological Solitons,...
Muneto Nitta(Keio U.)
Modulated VacuaTopological Solitons, Nonperturbative Gauge Dynamics and Confinement
20-21 July 2017, University of Pisa
arXiv:1706.02938 [hep-th], arXiv:1706.05232 [hep-th]
with Shin Sasaki (Kitasato) & Ryo Yokokura (Keio)
My connection with Ken and Pisa
2006 Started collaboration on topological solitons
(non-Abelian vortices and monopoles)
Visiting almost every year
Many of Ken’s students and postdocs become now
important collaborators and/or good friends of mine:Giacomo Marmorini -> cond-mat, now PD @ Keio
Walter Vinci -> quantum comp
Sven Bjarke Gudnason
Yunguo Jiang
Mattia Cipriani : PhD adviser -> plasma physics
--------------------------
Jarah Evslin
Chandrasekhar Chatterjee -> now PD @ Keio
Minoru Eto
Toshi Fujimori
Keisuke Ohashi
Keio U.
@ Yokohama, Kanagawa
in greater Tokyo
Topological
Science ProjectAimed to understand all
subjects of physics in terms of
Topology
5 years (2015-2020),
11 postdocs
Anyone here is very
welcome to visit!!
Keio U.
@ Yokohama, Kanagawa
in greater Tokyo
Topological
Science ProjectAimed to understand all
subjects of physics in terms of
Topology
5 years (2015-2020),
11 postdocs
Anyone here is very
welcome to visit!!
The great wave of Kanagawa
Figs from Basar,Dunne,Thies(‘09)
What is modulation?A field configuration modulated in a space (periodically)
Figs from Basar,Dunne,Thies(‘09)
History In a superconductor
Fulde & Ferrell (FF) (‘64)
Phase modulation
FFLO:
both phase & amplitude
Larkin & Ovchinnikov(LO) (‘64)
Amplitude modulation
HistoryIn a superconductor,
--- experimentally, some evidences but not conclusive
Other systems:
ultracold atomic fermion gases
--- experimentally, some evidences but not conclusive
History In chiral Gross-Neveu model in d=1+1
Chiral spiral
Phase modulation
Complex kink crystal
both phase & amplitude
Real kink crystal
Amplitude modulation
Exact self-consistent solution by Basar & Dunne (‘08)
History In Nambu-Jona-Lasino in d=3+1
Nakano & Tatsumi (‘04)
Chiral spiral
Phase modulation
Nickel (‘09) Real kink crystal
Amplitude modulation
In terms of Ginzburg-Landau effective theory
Nickel (‘09)
Higher derivative terms are needed
When , modulation can be favored0,4 bc 0 , ,6,6 cb cc
x
Analogous to frustrated magnet (Sutcliffe's talk)
Purpose of our work
(1) Modulation in relativistic field theory
Modulations considered so far in cond-mat., QCD
are ground states @ finite temperature/ density/
magnetic field, and so in non-relativistic theories.
(2) Modulation in supersymmetric field theory
Unusual Nambu-Goldstone boson
Goldstino
New mechanism of SUSY breaking
=
0
=
0
arXiv:1706.02938 [hep-th]
arXiv:1706.05232 [hep-th]
Cf )No-go theorem by Son
for relativistic fermion
condensates
Plan of talk
§1 Intoduction: What is modulation?
§2 Modulated vacua in bosonic theory
§3 Modulated vacua in SUSY
§4 Summary & Discussion
Plan of talk
§1 Intoduction: What is modulation?
§2 Modulated vacua in bosonic theory
§3 Modulated vacua in SUSY
§4 Summary & Discussion
Remember
m
222 t
m
m□
0,1,2,3m
Naively replace
Ghost
Ostrogradski
instability
, m
mfL m
mL 1
Ex) Nambu-Goto
relativisticnon-relativistic
Ostrogradski’s ghost instability
ghost
(wrong sign)
eliminating
M
1~
The highest order of must be odd2| |
Let’s consider a complex scalar field
nnL 222 ||||| |
22* | |)1( nn nL
nnn nLH 22** ||||)12()1( highest highest
Global stability condition
n
upper sign for
spatial stabilityodd n for
temporal stabilityThe simplest is 3n
3,2,1,0m0,, k
00||0 m00||0 1
Assume spatial
A model
Derivative corrections
)1,3(SO
Ordinary kineticwrong sign for 4th & correct sign for 6th
2
1 ||
2
1 ||
2
1 ||
Metastable(local
minimum)
Stable(degenerate)
Stable(global
minimum)
032 k
All cases
Local min @
2
1 || 042 k
042 k
042 k
1
0
1)( ipxex
2
0
2p
Modulate vacua
satisfying EOM
Spontaneous symmetry breaking
)1,3()()1()1,3()1( ,, SOPPUISOUG tzyx
translation
+ phase
)1,2())1(()1,2()1( , SOPPUISOUH tzyxx
How many Nambu-Goldstone (NG)?
Ivanov & Ogievetsky (‘75)
“Inverse Higgs mechanism”
Low & Manohar (‘02)
Only translation gives NG
)1,2(
)1,3()1(
ISO
ISOU
H
Gx
Order
Parameter
Space (OPS)
Inverse map of
More general solution
1
0
1)( ipxex preserves the highest symmetry
A vacuum alignment problem.(Quantum correction may pick up a state with the highest symmetry.)
Comment
Liner Analysis
VEV fluctuation
transverse
modulation
3,2,0m
Diagonalize 1M2M
1M
2M
Diagonalize in the modulated direction2M
NG mode
Higgs mode
No quadratic
kinetic term
gapless
higher
Plan of talk
§1 Intoduction: What is modulation?
§2 Modulated vacua in bosonic theory
§3 Modulated vacua in SUSY
§4 Summary & Discussion
Goldstino
=
0
=
0
Cf) BPS solitons (not vacuum)
BPS domain wall
SUSY transformation
0~1 F
00
New mechanism of SUSY breaking
2
1 ||
2
1 ||
2
1 ||
Metastable(local
minimum)
Stable(degenerate)
Stable(global
minimum)
032 k
All cases
Local min @
2
1 || 042 k
042 k
042 k
1
0
1)( ipxex
2
0
2p
Modulate vacua
satisfying EOM
2
1 ||
2
1 ||
2
1 ||
Metastable
Stable
Unstable
0E
0E
0E
|| 0PE
2
2,1
2
2,1~
Q
Q
SUSY algebraOrdinary
Goldstino
No Goldstino
Ghost
Goldstino
Stable
ljik (2,2) tensor
The unique term free from the auxiliary field problem
ljki
ljikDDDDd †††
),( 4
4 derivative term
I.L. Buchbinder, S. Kuzenko, and Z. Yarevskaya, NPB411, 665 (1994)A. T. Banin, I. L. Buchbinder, and N. G. Pletnev, PRD74, 045010 (2006)J. Khoury, J.-L. Lehners, and B. Ovrut, PRD83,125031 (2011)J. Khoury, J.-L. Lehners, and B. Ovrut, PRD84,043521 (2011) M. Koehn, J.-L. Lehners, and B. A. Ovrut, PRD86, 085019 (2012)C. Adam, J.M. Queiruga, J. Sanchez-Guillen, and A.Wereszczynski,
JHEP05 (2013)108C. Adam, J.M. Queiruga, J. Sanchez-Guillen, and A.Wereszczynski,
Phys. Rev. D 86, 105009 (2012)S. Sasaki, M. Yamaguchi, and D. Yokoyama, PLB718, 1(2012)
Ghost condensateGalileon
SUSY baby Skyrmion
SUGRA
suerpotential
LEEA of susyWZW
SUSY k-field theory
Expansion to quadratic orderx
0E
0E
0E
0C
0C
Correct sign
Wrong sign
(fermionic ghost)
No dynamics0C
C
Plan of talk
§1 Intoduction: What is modulation?
§2 Modulated vacua in bosonic theory
§3 Modulated vacua in SUSY
§4 Summary & Discussion
Summary
1.Generalized NG theorem
2. Gauging U(1) , generalized Higgs mechanism
3. More general models: higher order Skyrme model
4. Higher co-dimensional/ temporal modulation
5. Topological solitons in modulations
Discussion
1. Relativistic modulation
NG boson without quadratic term, gapless Higgs
2. Supersymmetric modulation
(usual, non-dynamical, ghost) Goldstino E(>0,=0,<0)
)1,1(
)1,()1(
dISO
dISOU
H
Gx
Order
Parameter
Space (OPS)
ZHG /1 1dS
Z HGd /1
vortices
Edge dislocation Screw dislocation
vortex⊥modulation
vortex //
modulation
Topological solitons in modulation
Crystal
小西さん、古稀(Koki=70 years old)、おめでとうございます。これまで、ありがとうございます。これからもよろしくお願いいたします。
Thank you for your attention
Notorious Problem: Auxiliary Field Problem
)()()(),( yFyyy
m acts on
Auxliary fieldChiral superfield mmm ixy
In general, F cannot be eliminated algebraically.
F may become dynamical DOF.
Is SUSY OK? Introduce of further fermion partner?
Is it always the case?
If not, how can we construct higher derivative term
without this problem?
H.D terms→
