First and second quantization theories of open p-brane and their spectra

Utilizing the free Polyakov action of open p-brane, we obtain the solution of satisfying the boundary conditions to Euler–Lagrange equation of the open p-brane, the first and second quantization theories of the p-brane are given. Further, we obtain a series of new multiple commutative relations between the different normal modes of the p  -brane, obtain the new lowering and raising multiple operators, and give a series of the new fundamental multiple commutative relations of the lowering and raising multiple operators in the state space. And then we mainly take p=3$p=3$ case for example to investigate the spectrum of the open 3-brane at different levels. Interestingly, we find three types of tachyon states including scalar states, vector states and 2-rank tensor states, respectively. Besides, the graviton fields, Kalb–Ramond fields, dilaton and photon states, 3-rank tensor states as well, appear at the same level in the open 3-brane model. For the spectrum of the p  -brane (p>3)$(p>3)$, one can do the whole analogous research on p=3$p=3$ except more complex.     

A proposal for M2-brane–anti-M2-brane action

We propose a manifestly SO(8)$\mathit{SO}(8)$ invariant BF type Lagrangian for describing the dynamics of M2-brane–anti-M2-brane system in flat spacetime. When one of the scalars which satisfies a free-scalar equation takes a large expectation value, the M2-brane–anti-M2-brane action reduces to the tachyon DBI action of D2-brane–anti-D2-brane system in flat spacetime.     

Mesons and Higgs branch in defect theories

We consider the defect theory obtained by intersecting D3- and D5-branes along two common spatial directions. We work in the approximation in which the D5-brane is a probe in the AdS₅×S⁵${\mathit{AdS}}_5\times S^5$ background. By adding worldvolume flux to the D5-brane and choosing an appropriate embedding of the probe in AdS₅×S⁵${\mathit{AdS}}_5\times S^5$, one gets a supersymmetric configuration in which some of the D3-branes recombine with the D5-brane. We check this fact by showing that the D5-brane can be regarded as a system of polarized D3-branes. On the field theory side this corresponds to the Higgs branch of the defect theory, where some of the fundamental hypermultiplet fields living on the intersection acquire a vacuum expectation value. We study the spectrum of mesonic bound states of the defect theory in this Higgs branch and show that it is continuous and gapless.     

Galilean anti-de-Sitter spacetime in Romans theory

The Romans type IIA theory is the only known example of 10-dimensional maximal supergravity where (tensor) fields are explicitly massive. We provide an example of a non-relativistic anti-de-Sitter NRadS₄×S⁶${\mathit{NRadS}}_4\times S^6$ background as a solution in massive type IIA. A compactification of which on S⁶$S^6$ gives immediately the prototype NRadS background in D=4$D=4$ which is proposed to be dual to ‘cold atoms’ or unitary fermions on a wire.     

Non-linear realizations,Goldstone bosons of broken Lorentz rotations and effective actions for p-branes

We consider the non-linear realizations of the Poincare group for p  -branes with local subgroup SO(1,p)×SO(D−(p+1))$\mathit{SO}(1,p)\times \mathit{SO}(D-(p+1))$. The Nambu–Goto p-brane action is constructed using the Maurer–Cartan forms of the unbroken translations. We perform a throughout phase space analysis of the action and show that it leads to the canonical action of a p-brane. We also construct some higher order derivative terms of the effective p-brane action using the MC forms of the broken Lorentz transformations.     

Localized fields on scalar global defects

We investigate the localization of modes on the worldvolume of a p  -brane embedded in (p+d+1$p+d+1$)-dimensional spacetime. The p  -brane here is such that its profile is regarded as a scalar global defect and the localized modes are scalar modes that come from the fluctuations around such defect. The effective action on the brane is computed and the induced potentials are typically ?⁴${?}^4$-type potentials that are flatter for lower d-dimensions. We also make a connection of such scalar global defects with black p-branes in certain limits.     

From local to global in F-theory model building

When locally engineering F-theory models some D7$D7$-branes for the gauge group factors are specified and matter is localized on the intersection curves of the compact parts of the world-volumes. In this note, we discuss to what extent one can draw conclusions about F-theory models by just restricting the attention locally to a particular seven-brane. Globally, the possible D7$D7$-branes are not independent from each other and the (compact part of the) D7$D7$-brane can have unavoidable intrinsic singularities. Many special intersecting loci which were not chosen by hand occur inevitably, notably codimension-three loci which are not   intersections of matter curves. We describe these complications specifically in a global SU(5)$SU\left(5\right)$ model and also their impact on the tadpole cancellation condition.     

A note on the UV behaviour of maximally supersymmetric Yang–Mills theories

The question of whether BPS invariants are protected in maximally supersymmetric Yang–Mills theories is investigated from the point of view of algebraic renormalisation theory. The protected invariants are those whose cohomology type differs from that of the action. It is confirmed that one-half BPS invariants (F⁴$F^4$) are indeed protected while the double-trace one-quarter BPS invariant (d²F⁴$d^2{F}^4$) is not protected at two loops in D=7$D=7$, but is protected at three loops in D=6$D=6$ in agreement with recent calculations. Non-BPS invariants, i.e. full superspace integrals, are also shown to be unprotected.