Centre for High Energy Physics (CHEP)
https://etd.iisc.ac.in/handle/2005/47
2021-09-27T05:05:51ZApplications of Holography
https://etd.iisc.ac.in/handle/2005/5294
Applications of Holography
Bala Subramanian, P N
This thesis consists of four parts. In the first part of the thesis, we investigate the phase
structure of Einstein-Maxwell-Scalar system with a negative cosmological constant. For
the conformally coupled scalar, an intricate phase diagram is charted out between the four
relevant solutions: global AdS, boson star, Reissner-Nordstrom black hole and the hairy
black hole. The nature of the phase diagram undergoes qualitative changes as the charge of
the scalar is changed, which we discuss. We also discuss the new features that arise in the
extremal limit.
In the second part, we do a systematic study of the phases of gravity coupled to an
electromagnetic field and charged scalar in flat space, with box boundary conditions. The
scalar-less box has previously been investigated by Braden, Brown, Whiting and York (and
others) before AdS/CFT and we elaborate and extend their results in a language more
familiar from holography. The phase diagram of the system is analogous to that of AdS
black holes, but we emphasize the differences and explain their origin. Once the scalar
is added, we show that the system admits both boson stars as well as hairy black holes as
solutions, providing yet another way to evade flat space no-hair theorems. Furthermore both
these solutions can exist as stable phases in regions of the phase diagram. The final picture of
the phases that emerges is strikingly similar to that of holographic superconductors in global
AdS, discussed in part one. We also point out previously unnoticed subtleties associated to
the definition quasi-local charges for gravitating scalar fields in finite regions.
In part three, we investigate a class of tensor models which were recently outlined as potentially
calculable examples of holography, as their perturbative large-N behavior is similar
to the Sachdev-Ye-Kitaev (SYK) model, but they are fully quantum mechanical (in the sense
that there is no quenched disorder averaging). We explicitly diagonalize the simplest nontrivial
Gurau-Witten tensor model and study its spectral and late-time properties. We find
parallels to (a single sample of) SYK where some of these features were recently attributed
to random matrix behavior and quantum chaos. In particular, after a running time average,
the spectral form factor exhibits striking qualitative similarities to SYK. But we also observe
that even though the spectrum has a unique ground state, it has a huge (quasi-?)degeneracy
of intermediate energy states, not seen in SYK. If one ignores the delta function due to the
degeneracies however, there is level repulsion in the unfolded spacing distribution hinting
chaos. Furthermore, the spectrum has gaps and is not (linearly) rigid. The system also has
a spectral mirror symmetry which we trace back to the presence of a unitary operator with
which the Hamiltonian anticommutes. We use it to argue that to the extent that the model
exhibits random matrix behavior, it is controlled not by the Dyson ensembles, but by the
BDI (chiral orthogonal) class in the Altland-Zirnbauer classification.
In part four, we construct general asymptotically Klebanov-Strassler solutions of a five
dimensional SU(2) SU(2) Z2 Z2R truncation of IIB supergravity on T1;1, that break
supersymmetry. This generalizes results in the literature for the SU(2) SU(2) Z2 U(1)R
case, to a truncation that is general enough to capture the deformation of the conifold in
the IR. We observe that there are only two SUSY-breaking modes even in this generalized
set up, and by holographically computing Ward identities, we confirm that only one of them
corresponds to spontaneous breaking: this is the mode triggered by smeared anti-D3 branes
at the tip of the warped throat. Along the way, we address some aspects of the holographic
computation of one-point functions of marginal and relevant operators in the cascading gauge
theory. Our results strengthen the evidence that if the KKLT construction is meta-stable, it
is indeed a spontaneously SUSY-broken (and therefore bona fide) vacuum of string theory.
Applications of Moonshine Symmetry in String Theory
https://etd.iisc.ac.in/handle/2005/5001
Applications of Moonshine Symmetry in String Theory
Chattopadhyaya, Aradhita
In this thesis we study the applications of Mathieu moonshine symmetry to compacti cations of supersymmetric
string theories. These theories are compacti ed on a 6 dimensional manifold K3 T2. The
main ingredient in this study is a topological index called twisted elliptic genus. For a super-conformal
eld theory whose target space is a K3 there can be several automorphisms on K3 which are related
to Mathieu group M24. Under these automorphisms it was observed that the twining genera of the
twisted elliptic genus of K3 could be written in terms of the short and long representations of N = 4
super-conformal algebra and the characters of M24 [1, 2, 3]. We compute the twisted elliptic genus in
every sector for 16 of these orbifolds using the results of [2].
Firstly we study the heterotic compacti cations of N = 2 super-symmetric strings compacti ed on
orbifolds of K3 T2 and E8 E8 where g0 is an action on K3 corresponding to [M24] along with a 1=N
shift on one of the circles of T2. We compute the gauge and gravitational threshold corrections in these
theories. Here we need a topological index called the new supersymmetric index. The un-orbifolded
result for K3 was known for gauge couplings in [4] and the gravitational ones were computed in [5]. We
observe that the di erences in gauge couplings can be written in terms of the twisted elliptic genus of
K3 for standard embeddings. For non-standard embeddings we studied two orbifold realizations of K3
as T4=Z2 and T4=Z4 and computed the threshold di erences. The result could be written in terms the
twisted elliptic genus of K3 and the elliptic genus of K3. From the gravitational corrections we predict
the Gopakumar Vafa invariants and the Euler character for the dual Calabi Yau geometries. We also
observe that the conifold singularities of these manifolds are manifested in twisted sectors only and only
the genus zero Gopakumar-Vafa invariants at those points are non-zero.
Secondly we study the properties of 1/4 BPS dyons in type II string compacti ed on K3 T2 orbifolded
with an action of g0 which corresponds to automorphisms of K3 corresponding to the conjugacy classes of
Mathieu group M24 and a 1=N shift in one of the circles of T2. For these compacti cations the counting
function for these dyons can be computed from Siegel modular forms given by the lift of the twisted
elliptic genus. These give the correct sign as predicted from black hole physics as conjectured by Sen [6].
We also study the properties of 1/4th BPS dyons in type II string theory compacti ed on Z2 and Z3
orbifolds on T6 with 1=N shift in one of the S1 and encountered some violations to this conjecture which
points to the existence of non-trivial hair modes. We associate mock modular forms corresponding to
single centred black holes and extend the work of Dabholkar-Murthy-Zagier [7] to these orbifolds of K3
and also for the toroidal orbifolds.
In computing the twisted elliptic genus and new super-symmetric index in various twisted sectors we
encounter several identities between some 0(N) modular forms. With a bit more analysis we determine
the exact location of the zeros of some weight 2 Eisenstein series of 0(N) in the fundamental domain
of 0(N) where N = 2; 3; 5; 7. The location of their zeros were controlled by those of Eisenstein series of
weight 4 and 6.
Aspects of conformal field theories at finite temperature
https://etd.iisc.ac.in/handle/2005/5238
Aspects of conformal field theories at finite temperature
Dutta Chowdhury, Subham
In this thesis we have studied broadly two aspects of thermal field theory. We began by examining how
the macroscopic system (described by relativistic hydrodynamics) behalves in presence of microscopic
anomalies. We are able to relate macroscopic transport coefficients to the anomalous conservation equations
of the microscopic theory. It is to be noted that, using the perturbative methods that we develop,
we are able to relate both the mixed and pure gravitational anomalies to their respective transport coe
fficients. Our results agree with other methods used to study this relationship. Using our perturbative
approach, we are also able to understand the breakdown of the replacement rule for gravitino systems.
Global anomalies instead of perturbative anomalies can also be used to x the macroscopic transport
coefficients. By computing the global anomalies associated with particular systems, we were able to
write down thermal effective actions which reproduce the anomalies. We show that such effective actions
can be used to compute the transport coefficients and obtain a match with our perturbative results. We
also provide a topological understanding of the replacement rule. As a further check of our formalism,
we compute perturbatively using the formalism developed in [11], the anomalous transport coefficient
(corresponding to pure gravitational anomaly) for self dual tensors in d = 6 and obtain a match with
the global anomaly result.
In the second part of the thesis we look at constraints that can be placed on spectral densities in
a conformal field theory at fi nite temperature. Sum rules provide important constraints on spectral
densities of any quantum field theory. We relate the weighted integral of spectral densities over frequency
to the energy density of the theory. We show that the proportionality constant can be written down
in terms of Hofman-Maldacena variables t2 and t4, which determine the three point function of stress
tensors of a parity preserving CFT. For CFTs dual to two derivative Einstein gravity, we nd agreement
of our sum rule derived from general conformal invariance with holographic methods. We also obtain
correction to the holographic shear sum rule for theories with quadratic curvature corrections to the
Einstein gravity.
We extend the conformal collider physics formalism developed by Maldacena et al to study three point
functions involving a stress tensor T, a U(1) current j, in 2 + 1 dimensional parity violating conformal
field theories. We show that large N Chern Simons theories coupled to fundamental fermions/ bosons
saturate our derived bounds. This is consistent with the observations that the scaling dimensions of spin
operators in these theories saturate the unitarity bound ( s s + 1) and hence perhaps the conformal
collider bounds as well.
Aspects of Heavy Supersymmetry
https://etd.iisc.ac.in/handle/2005/4985
Aspects of Heavy Supersymmetry
Lamba, Priyanka
The recent discovery of a Higgs boson with a mass around 125 GeV, taken together with experimental results from flavor factories, dark matter direct detection, and searches for SUSY particles in the LHC suggest that supersymmetric particles could be heavy in the range of multi-TeV beyond the reach of LHC. In typical supersymmetry breaking models, supersymmetry breaking in the hidden sector is parametrised by a single spurion field mediated at a specific scale, which we call single scale breaking. Although in this case, heavy-scale SUSY breaking models have very large fine-tuning, they are simultaneously economic from the phenomenological perspective. In a typical heavy-scale SUSY model, the gauginos and higgsinos are still around the TeV scale since they can be protected by chiral symmetry, and contain a dark matter candidate. The heavy sfermions relax bounds coming from flavor changing processes and CP violation, and also increase the radiative corrections to the Higgs mass.
The aim of the thesis is to study the implications of the heavy supersymmetry while relaxing the assumption of single scale mediation for supersymmetry breaking. In the first study of this thesis, we consider MSSM with N_HS sequestered hidden sectors at a high scale, contributing to supersymmetry breaking. Each hidden sector communicates supersymmetry breaking to the visible (MSSM) sector through effective interactions. Considering a random distribution for the spurion parameters leads a normal distribution for the soft parameters with mean values and standard deviations that are analytically computable. We study the probability of getting Higgs mass in the correct range while having successful electroweak symmetry breaking. We show that the probability
distribution is peaked when the quanta of supersymmetric breaking is around m ̃=220 GeV for the parametrisation of the spurion fields we have considered. For these regions we study the supersymmetric spectrum.
In the next work, we study fine-tuning, where each of the spurion's contribution is parametrised as m ̃M_Pl c_α. We treat each spurion field as an independent source of supersymmetry breaking. Requiring minimal fine tuning from each sector, gives C_r^((2N_HS-1) ) solutions. In fact, we find there is only one solution independent of all the RG coefficients, where all the sectors
contribute coherently. The fine-tuning becomes almost negligible even with a small number of hidden sectors, N_HS=20. The coherent SUSY framework also has a well-tempered dark matter region due to high cancellation in gaugino soft terms. It also has regions of coannihilation with charginos.
A concrete realisation with a large number of hidden sectors is presented in the next chapter, where we consider a Stringy landscape like scenario inspired by Bousso-Polchinski's solution to the cosmological constant problem. The spurion fields are given in terms of quantized four form fluxes whose vacuum expectation values set the supersymmetry breaking scales. Coupled to supergravity, we compute the soft spectrum in this framework assuming a uniform distribution for the quantized flux charges. We have shown that this framework naturally leads to a suppression of the flavor violating entries as 1/√(N_HS ) There is further suppression due to the renormalisation group running at the weak scale, especially for the hadronic mass insertions.
In the last part of the thesis, we consider single scale supersymmetry breaking and study the implications of the heavy spectrum in the context of SUSY GUT. We consider SUSY SU(5) with a novel decoupling scenario named flavored 'split-generation', where O(1) flavor violation can be present in the model. In this scenario, first and second generation of sfermions are assumed to be heavy (order of 10s of TeV) and the remaining SUSY spectrum lies around a few TeV. Two codes have been developed for this work. 1) A modified version of SuSeFLAV has been developed where
we calculate the full two-loop $\beta-$coefficients and one-loop threshold at the two different scales. 2) A code for full SUSY SU(5) proton decay analysis. In this work, we study gauge coupling unification and the two dominant proton decay channels ( p→e^+ π^0 and p→K^+ ν ̅) both with and without flavor mixing in a heavy and light (third) generation. The flavored ‘split-generation' scenario leads to peculiar cancellations in the amplitudes. The rate of p→e^+ π^0 is highly sensitive to amount of flavor violation present as it opens the gluino contribution to the amplitudes. On the other hand, we find that sensitivity of the rates of p→K^+ ν ̅ is related to the flavor of the neutrino emitted. The implications for future proton decay experiments like Hyper-K, DUNE and JUNO are reported.