string pair production in non homogeneous backgrounds
TRANSCRIPT
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String pair production in non homogeneous backgrounds
Stefano Bolognesi
Università di Pisa and INFN
CAQCD16
arXiv:1601.04785 in collaboration with E. Rabinovici and G.Tallarita
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Plan of the talk
Introduction to pair production, worldline formalism and non homogeneous backgrounds in field theory
• String theory examples of pair production which are treatable with the ‘‘worldsheet instanton’’ technique:
1) String suspended between D-branes
2) Holographic Schwinger effect
• Effects of non-homogeneous backgrounds on string production
Work in collaboration with E. Rabinovici and G.Tallarita
z
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Plan of the talk
Introduction to pair production, worldline formalism and non homogeneous backgrounds in field theory
String theory examples of pair production which are treatable with the ‘‘worldsheet instanton’’ technique:
1) String suspended between D-branes
2) Holographic Schwinger effect
• Effects of non-homogeneous backgrounds on string production
Work in collaboration with E. Rabinovici and G.Tallarita
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Plan of the talk
Introduction to pair production, worldline formalism and non homogeneous backgrounds in field theory
String theory examples of pair production which are treatable with the ‘‘worldsheet instanton’’ technique:
1) String suspended between D-branes
2) Holographic Schwinger effect
Effects of non-homogeneous backgrounds on string production
Work in collaboration with E. Rabinovici and G.Tallarita
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Pair production
E
q* q
Schwinger effect is non-perturbative pair production of q-q* due to
electric background
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Pair production
E
q* q
Schwinger effect is non-perturbative pair production of q-q* due to
electric background
This effect becomes significant at
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Worldline instanton
Afflek-Alvarez-Manton 82
One searches for stationary solution of the Euclidean worldline action
Same trajectories of a charged particle moving in a background magnetic field
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Worldline instanton
Afflek-Alvarez-Manton 82
For a constant background the solution is given by a circular trajectory
with action consistent with Schwinger formula
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Pair production in QFTSolutions are “extremal” circular orbits with radius R
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Pair production in QFT
They describe the tunneling in Minkowsky
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Non homogeneous background
SauterBrezin-Itzykson 70…
Schwinger effect becomes significant at
Non homogeneous backgrounds can lower this value significantly!
Direct observation of the Schwinger effect may possible in the near future
with the use of strong laser pulses
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Time-dependent pulse
The simplest case is a single pulse of electric field dependent on time only
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Time-dependent pulse
The simplest case is a single pulse of electric field dependent on time only
The Euclidean corresponding field is
We already see that there should be enhancement
of pair production if the instanton is finite!
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Time-dependent pulse
Dunne-Shubert 05
The exact solution is:
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Time-dependent pulse
Dunne-Shubert 05
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Time-dependent oscillation
Another important case is an oscillating electric field with fixed frequency
The Euclidean corresponding field is
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Time-dependent oscillation
The exact solution is:
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Summary of Results
Worldline action comparison:
Both time dependent actions
are lower than the “locally
constant” approximation.
This indicate enhancement of
pair production
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Summary of Results
Worldline action comparison:
Continuous interpolation
between “tunnelling” and
“photon absorption”
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Space-dependent pulse
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Space-dependent oscillation
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Summary of Results
For space dependent
backgrounds is just the
opposite
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Pair production in string theory
Fradkin-Tseytlin 85Burgess 87Bachas-Porrati 92…
In string theory there is a critical value where the barrier for pair
production disappears and the vacuum is “catastrophically’’ unstable
Not much is known about string pair production in non homogeneous
backgrounds
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String suspended between two D-branes
We look for a case where pair production
can be studied with the “worldsheet
instanton” technique
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String suspended between two D-branes
We look for a case where pair production
can be studied with the “worldsheet
instanton” technique
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Minimal surface solution
For constant background, and so circular symmetry:
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Minimal surface solution
For constant background, and so circular symmetry:
The solutions are the well known “catenaries” minimal surface
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String suspended between two D-branes
For R sufficiently large there are two solutions: “thick neck” and “thin neck
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String suspended between two D-branes
For R sufficiently large there are two solutions: “thick neck” and “thin neck
Critical field is as expected:
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Time-dependent setup
We work in cylindrical cordinates
and have to find a function of two variables
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Time-dependent setup
The boundary term is given by the specific choice of background electric field
We use Fourier angular decomposition and Chebyshev polynomials in z
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Solution for small frequency case
Pulse
with
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Solution for small frequency case
Oscillation
with
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Solution for higher frequency
String effects are expected to be important when E is big enough
Non-homogeneity effects are expected to be important when E is small enough
So we need to increase omega to see effects that are both “stringy”
and related to non-homogeneity
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Solution for higher frequency
Pulse
with
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Solution for higher frequency
Pulse
with
“Double” enhancement of pair production
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Solution for higher frequency
Oscillation
with
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Pulse
Small E string effects (?)
As E->0 the area inside the loop goes to zero and becomes smaller thanworldsheet area
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Pulse
Small E string effects (?)
As E->0 the area inside the loop goes to zero and becomes smaller thanworldsheet area
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Space dependent pulse
Pulse
with
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Space dependent oscillation
Oscillation
with
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We consider N=4 SYM in the Coulomb phase
This is the U(1) of the Schwinger effect
Holographic Schwinger effect
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We consider N=4 SYM in the Coulomb phase
Holographic Schwinger effect
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Holographic Schwinger effectThe dictionary is the usual
plus the relation for the W mass
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Holographic setting
The DBI action predicts the string to break down at “local” string scale
This is translated into a genuine QFT scale
This is the value where the barrier for the pair production drops to zero in the QFT!
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Holographic worldsheet instanton
B.-Kiefer-Rabinovici 12
In holography, the instanton is a Wilson loop attached to the D3 brane
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Holographic worldsheet instanton
Minimal surface is a spherical cap
Boundary condition
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Holographic worldsheet instanton
The action vanishes when the spherical cap is
tangent to the D-brane
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Tunneling barrier exists only below a certain critical field
Holographic worldsheet instanton
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Time-dependence setup
we work in cylindrical cordinates
and have to find a function of two variables
As before:
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Time-dependence setup
Boundary conditions are:
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Some solutions
Pulse
with
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Some solutions
Oscillation
with
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Confining background
Hard-wall geometry:
Confining string
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Confining background
At the field
we have a transition in the type
of worldsheet solution:
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Low critical field in confing background
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Low critical field in confining background
The interpretation of the “low” critical field in Minkowski:
When the electric field is not strong enough
to overcome confinement
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Low critical field and time-dependence
The critical low field is in general modified by the frequency omega.
We show a clear example in which it vanishes!
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Low critical field and time-dependence
Maximum holographic z for low E:
Unlike the constant background case,
z max is bounded from above:
oscillation
pulse
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Low critical field and time-dependence
oscillation
pulseIf the confinement scale is so that
The Euclidean worldsheet is always contained inside the physical space.
Pair production happen irrespectively on how small is E.
Photons energy is enough to produce glueballs and charged particles are intermediary states
Maximum holographic z for low E:
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Conclusion
• We studied two cases of string pair production with the technique of Euclidean worldsheet instanton
• With this technique we can define the problem on non homogeneous backgrounds and solve PDE numerically
• String nature and non homogeneity work together when omega is big enough; for time dependent backgrounds they enhance even further the pair production
• Pair production in confining background is highly modified by the non-homogeneity. In particular the low critical field can disappear