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In recent years, Erdogan’s rising authoritarian tendencies at home coincided with the hardening of his positions in the country’s foreign relations. From Libya to Syria to Greece to Iraq to Azerbai...

We consider free higher derivative theories of scalars and Dirac fermions in the presence of a boundary in general dimension. We establish a method for finding consistent conformal boundary conditions in these theories by removing certain boundary primaries from the spectrum. A rich set of renormalization group flows between various conformal boundary conditions is revealed, triggered by deformations quadratic in the boundary primaries. We compute the free energy of these theories on a hemisphere, and show that the boundary $a$-theorem is generally violated along boundary flows as a consequence of bulk non-unitarity. We further characterize the boundary theory by computing the two-point function of the displacement operator., 49 pages, 2 figures. v2: References and minor comments added. v3: Comments added

The recent emergence of the modern conformal bootstrap method for the study of conformal field theories (CFTs) has enabled the revisiting of old problems in classical critical phenomena described by three-dimensional CFTs. The study of such CFTs with $O(m)^n \rtimes S_n$ global symmetry, also known as MN models, is pursued in this work. Systems of mixed correlators involving scalar operators in two different representations of the global symmetry group are considered. Isolated allowed regions are found in parameter space for various values of $m$ and $n$. These "islands" can be separated into two qualitative groups: those close to the unitarity bound and those further away. As a by-product of our analysis generic tensor structures required to bootstrap any $G^n \rtimes S_n$ theory with $G$ arbitrary are worked out., 29 pages, 14 figures. v2: 30 pages, 15 figures. Comments added. Some rearranging of sections for clarity of presentation. New Fig. 7 and additional information added to Fig. 9 v3: some additional clarifications

The tensorial equations for non trivial fully interacting fixed points at lowest order in the $\varepsilon$ expansion in $4-\varepsilon$ and $3-\varepsilon$ dimensions are analysed for $N$-component fields and corresponding multi-index couplings $\lambda$ which are symmetric tensors with four or six indices. Both analytic and numerical methods are used. For $N=5,6,7$ in the four-index case large numbers of irrational fixed points are found numerically where $||\lambda ||^2$ is close to the bound found by Rychkov and Stergiou in arXiv:1810.10541. No solutions, other than those already known, are found which saturate the bound. These examples in general do not have unique quadratic invariants in the fields. For $N \geqslant 6$ the stability matrix in the full space of couplings always has negative eigenvalues. In the six index case the numerical search generates a very large number of solutions for $N=5$., Comment: 50 pages, 6 figures. v2: 53 pages, 6 figures; Expanded discussion of N=4 case including splitting of fixed point at order $\varepsilon^2$; v4: Minor corrections and additions

The Greek military regime’s policy towards Communist countries from 1969 until 1973 was a constellation of political, economic and geopolitical factors. The Colonels’ non-political relationship with the “hateful communists” was based on reasons related to domestic propaganda and the regime’s attempt to create the impression of an independent foreign policy. Despite the downside of the legitimisation of a staunch anti-Communist dictatorial regime, Eastern European countries embraced Greece’s opening, with a view to end their marginalisation following the Prague Spring. In fact, it served very effectively propaganda purposes for both sides. The Greek military regime could boast of its independent foreign policy outside the country and unsettle the leftist opposition inside. The Soviet Bloc demonstrated its technological and economic achievements and entertained the international outcry against the Warsaw Pact invasion of Czechoslovakia in 1968. In the Soviet propagandist discourse, the Western capitalist states flattered them, to try to establish ties with Communist states despite their ideological aversion, in order to gain benefits. Moral indignation was not allowed to affect the self-interest of the countries involved. In retrospect, it can be easily concluded that it provoked much more perplexity and concern than it really deserved. Undoubtedly, it was marked by some spectacular events, such as the diplomatic normalisation of relations with some countries to which the Greek state had had only limited ties or no ties at all, the clinching of trade deals, as well as the exchange of official visits at the highest level. However, it brought limited tangible results in economic terms (the trade volume declined compared to the previous period) and, contrary to fears in the Western camp amid serious political unrest in the Middle East, North Africa and Europe threatening to disrupt the power equilibrium in the wider region, did not affect Greece’s position in the NATO Alliance at all.

Greece’s Ostpolitik, i.e. the opening of the Greek State to the Communist countries during the Cold War, though so far has been a terra incognita of European history and politics, was an important chapter of the Cold War international relations. Ostpolitik, in its literal sense, means “Eastern politics” and relates to the policy of conducting affairs with the Eastern European states including the Soviet Union. From the late 1960s onwards, the term Ostpolitik has shifted towards representing a policy of detente with the Eastern European countries, based on the acceptance of Europe’s post-war division and the struggle for a regulated coexistence in a world of Blocs.

Greece’s comprehensive opening to the Communist world began in 1975, after the restoration of parliamentarism and the Cyprus tragedy in the Summer of 1974. The improvement of Turkish-Soviet relations since the mid-1960s and the dramatic deterioration of the Greek-Turkish relations, while Greece was not a member of the NATO military structure, were the main drivers of the new foreign policy course. Greece’s withdrawal from the NATO integrated military command as a reaction against “Alliance inertia” during the Turkish invasion in Cyprus in July and August 1974, was a seminal move, albeit not a well thought out one. The dissatisfaction with allies, especially the naive perception that NATO had failed to guarantee Greek security against Turkish aggression, ending up in Greece’s withdrawal from NATO, increased anti-Americanism and affected Greek society’s perceptions of global politics. The well resonated demand for more independence from the United States and a multidimensional foreign policy dovetailed with Prime Minister Konstantinos Karamanlis’s new security concept. In the context of the new multidimensional foreign policy, an active Ostpolitik was regarded as a complement to the then main foreign policy objective of the country, the accession to the European Community. Apart from it, the escalation of Greek-Turkish tensions rendered it imperative for Greece to ensure the neutrality of the Communist Balkan countries in the event of a war. As Greece was in great need of diplomatic support in its confrontation with Turkey on Cyprus and the Aegean, Karamanlis envisaged the possibility of a Balkan cooperation as a counteract to the Turkish assertive policy. Against this background and by looking carefully at the meetings, agreements and diplomatic moves Greece undertook in this period towards the various Communist countries, it becomes clear that almost all of them took place immediately after analogous Turkish moves. Athens endeavoured to ensure that Turkey did not gain more advantages in its relations with the Soviet Bloc than Greece, that, in turn, would frustrate Athens’s strategy to counterbalance Turkish aggression through new Alliances.

Notably, Greece’s strategic location has been both an asset and a liability. Its real and enduring strategic importance for both the Western and the Soviet Alliance during the Cold War derived from many political and geographic conditions and circumstances. Since it laid directly across Soviet sea and air lines of communication to the Mediterranean and beyond, it offered vantage points for the United States and NATO from electronic reconnaissance and surveillance. Greece provided continuity to the Southern region of the Alliance, not only for the purpose of military communications, but also in protecting Italy from the East and Turkey from the West. The greatest Greek strategic asset, however, was its land mass which, along with the nearly 3000 Greek islands of the Aegean gave strategic depth in Alliance defence.

From the mid of 1950s onwards, Greece initiated a policy of rapprochement, a quasi-Ostpolitik, towards the Communist countries, aimed at promoting simultaneously several goals: economic, geopolitical and security-oriented ones. Despite serious security concerns, Athens decided to adhere to the primacy of diplomacy, meaning placing more emphasis on political and diplomatic dialogue than on military deterrence. This was necessitated by the inferiority of the Greek armed forces compared to these of the Soviet Bloc, and the belief that it was not absolutely certain that Greece’s Western allies would come to its aid in the event of a coordinated attack by the Warsaw Pact. Another important driver for change of the foreign policy paradigm was the economy, and especially trade. Until the late 1960s, Greek exports consisted almost exclusively of agricultural products and raw materials, with tobacco and raisins covering almost half of their total value. Demand for these products in Western markets was usually weak and competition strong. This left Greece with huge surpluses in the agricultural sector, further straining the trade deficit. So, trade with the Eastern Europe was a vital outlet: agricultural products were bartered for oil, wood, meat and capital equipment. On the other hand, Greece was ascribed enhanced strategic value in the framework of the 1956 Soviet “peace offensive” towards the West. This course, coordinated with other Communist countries’ policy in the Eastern Mediterranean, aimed at loosening Greece’s, Turkey’s and Yugoslavia’s ties to the West. Against this background, Greece’s relations with most of Soviet Bloc countries improved rapidly, mainly at the economic level, heralding a full normalisation of the strained political relations. In the late 1950s, however, when Athens decided to give its consent to the deployment of nuclear weapons on Greek territory, the Soviet “peace offensive” was transformed into a real offensive. The Soviet Bloc staged an aggressive political offensive against Greece threatening to resort to serious reprisals should the Greek government go ahead with the installation of the US nuclear missiles. The Greek government stood its ground, but a lack of confidence was entrenched in Greece’s relations with the Soviet Bloc, that remained strong until the late 1960s, despite some progress in the economic and cultural fields.

In contrast to other Western European countries in which the Eighties were characterised by the cultural dominance of the “New Right”, Greek politics was dominated in the 1980s by the rise of the Greek Socialist Party (PASOK) which came to power in October 1981. Greece’s foreign and security policy towards the Soviet Bloc in the 1980s was for the most part a continuation of the Ostpolitik pursued by Greece’s conservative governments in the 1970s. An important component of the new era in the external relations of the country was the restrictive framework within which it played out. Contrary to the 1974–1981 period, the Greek Socialist era coincided with the hot phase of the Cold War in the first half of the 1980s, as well as with Greece’s reintegration into the NATO military command and accession to the European Community. In this framework, Greece’s new Prime Minister Andreas Papandreou’s opening to the Eastern European countries was not as skilful as Karamanlis’ policy. While Greece’s Ostpolitik in the 1970s did not precipitate any clash with the Western camp, Athens’ very active analogous policy in the 1980s burdened Greece’s relationship with its European and transatlantic allies. With his unprecedented opening to the Socialist camp and his radical anti-Western rhetoric and demagoguery, Papandreou became the “enfant terrible” within the Western Alliance. His resolute stance towards Turkey in a period of dramatic escalation of the Greek-Turkish conflict threatened to disrupt the balance of power in the Eastern Mediterranean, terrifying the NATO Alliance. In fact, US officials appeared by the end of the decade, after the two countries came again to the verge of a war, to have come to the conclusion that Greece and Turkey could hardly become US allies in a NATO engagement in South-Eastern Europe. On the other hand, the Soviet Bloc’s policy towards Greece since 1974 resembled that towards Turkey. It was characterised by economic benevolence, patience, gradual building of confidence and skilful exploitation of Greek disillusionment and dissatisfaction with NATO.

Fixed points in three dimensions described by conformal field theories with $MN_{m,n}= O(m)^n\rtimes S_n$ global symmetry have extensive applications in critical phenomena. Associated experimental data for $m=n=2$ suggest the existence of two non-trivial fixed points, while the $\varepsilon$ expansion predicts only one, resulting in a puzzling state of affairs. A recent numerical conformal bootstrap study has found two kinks for small values of the parameters $m$ and $n$, with critical exponents in good agreement with experimental determinations in the $m=n=2$ case. In this paper we investigate the fate of the corresponding fixed points as we vary the parameters $m$ and $n$. We find that one family of kinks approaches a perturbative limit as $m$ increases, and using large spin perturbation theory we construct a large $m$ expansion that fits well with the numerical data. This new expansion, akin to the large $N$ expansion of critical $O(N)$ models, is compatible with the fixed point found in the $\varepsilon$ expansion. For the other family of kinks, we find that it persists only for $n=2$, where for large $m$ it approaches a non-perturbative limit with $\Delta_\phi\approx 0.75$. We investigate the spectrum in the case $MN_{100,2}$ and find consistency with expectations from the lightcone bootstrap., Comment: 23 pages, 8 figures. v2: Minor emendations, additions and clarifications